In 1937, it was decided in Germany that a new type of torpedo boat, the Type 37, would be built. Nine ships were built, T13-21. The first, T13, was completed in 1939 and the last, T21, was ready to be launched in 1941. The original armament consisted of a 105 mm cannon, 2 automatic cannons with 20 mm ammunition, 2*3 533 mm torpedo tubes and 30 mines. At the end of 1944, the torpedo boats in the 3rd Torpedo Boat Flotilla, which included T13, received new armament when the aft torpedo tubes were replaced with 37 mm automatic cannons for defense against air attacks.

The commander on board T13 was Kapitänleutnant Gotzmann. During 1941, the ship was used for training and combat training before being transferred to France in January 1942 to take part in Operation Zerberus on 11-13 February.

Late in the evening of 11 February, the German ships Prinz Eugen, Scharnhorst and Gneisenau left Brest in France to go to Wilhelmshaven in Germany via the English Channel. The German ships were escorted by, among others, T13. Until the morning of the 12th, the convoy escaped attack completely, but later in the day, when passing Dover, it was attacked by British aircraft and coastal artillery, but it managed to reach Germany without major damage. Prinz Eugen escaped completely unharmed. Scharnhorst was damaged after being hit by two mines but was able to get to Germany and later be repaired. Gneisenau was hit by a mine but was only slightly damaged. 17 German aircraft were shot down. T13 and another torpedo boat, Jaguar, suffered minor damage from shrapnel and machine gun fire. The Germans shot down 42 British aircraft and severely damaged a British ship.

T13, which was quickly repaired, soon continued its missions as an escort ship up to Norway in March 1942. In March 1943, it returned to Germany for various repairs at the shipyard in Hamburg. In July, it was finished and from August onwards, T13 served as a training ship and Gotzmann was replaced by Kapitänleutnant Seyfried as commander aboard T13.

In early 1944, T13 was placed back in active service, now under the command of Oberleutnant Rönnau and under him he had 155 men, six of whom were officers, and acted as escort for various ships on their way through the Kattegat and Skagerack. On 21 May, it escorted Theodore Riedel and Friedrich Ihn on their way from Gdynia up through the Kattegat and Skagerack.

On 2 September 1944, Finland broke off diplomatic relations with Germany, forcing the 3rd Torpedo Boat Flotilla to leave Finnish territory. Together with T18 and T20, it left Finland on 15–17 September. Just north of Tallinn, the ships were attacked by Russian aircraft and T18 was sunk. On 23 September, the last German ships left Tallinn, and Russian aircraft attacked on two occasions, but the German ships escaped unharmed.

During the period 6–13 October, T13, together with T16, T20 and T21, acted as escort for Prince Oygen and Lyttsov. The torpedo boats patrolled to prevent submarine attacks.

In November 1944, the 3rd Torpedo Boat Flotilla was based in Gdynia and later, in mid-December, it returned for missions in the Kattegat and Skagerrak. Missions in the Baltic Sea were limited to occasional convoy escort duties.

During January until March 1945, escort missions continued for convoys in the Kattegat and Skagerrak. The British, who deciphered the German encrypted messages, used information about where the convoys were going and attacked the convoys with bomber aircraft. However, T13 managed to avoid damage on several occasions.

However, in early April, luck turned and during the night between 9 and 10 April, T13 was in the Kattegat together with T16 and T17 where it was part of the escort for a convoy heading north. The convoy included Hansal, which at the time was carrying submarine ammunition. On the morning of 10 April, the convoy was attacked by British Halifax bombers from the 58th and 502nd. The attack lasted until 0245 and 20 people died in the attack. T-13 and Hansa 1 sank at 0304. T-16 was badly damaged but managed to reach Fredrikshamn where the ship was later destroyed in another British air raid. This was the last torpedo boat operation of the war.