Gantu's ship is a Galactic Federation Star Cruiser 1838 that Gantu uses as a personal transport.
In Lilo & Stitch, Gantu is sent by the Grand Councilwoman to capture Stitch after Jumba and Pleakley failed to do so, and he makes to leave Earth. Nani is shocked to see Gantu putting Lilo and Stitch in a container pod and taking off in the ship. Stitch, however, escapes from the container before the ship takes off. Stitch, with help from Jumba's ship and by launching a gas tanker truck out of a volcano, is able to free Lilo and stop Gantu. Gantu shoots at the ship, causing it to explode.
In Stitch! The Movie, Gantu abducts Jumba in his rebuilt ship for interrogation of the experiment pods upon noticing one pod that fell from its container, and after Jumba refused to reveal the location of the others. On Gantu's ship, Hämsterviel tries to intimidate Jumba. When Jumba refuses to spill the beans, Hämsterviel activates Experiment 625 to attack him. Fortunately for Jumba, while 625 has all of Stitch's powers, he is incredibly lazy, a terrible coward, and prioritizes sandwiches above all else. When Hämsterviel ransoms Jumba for Experiment 221 (an experiment that Lilo and Stitch had activated earlier), Lilo and Stitch manage to save Sparky (the name Lilo gave the experiment) and rescue Jumba, while Hämsterviel and Gantu climb back into the ship with the container of experiments. In a last attempt to stop Hämsterviel, Lilo and Stitch stow away on the ship as it leaves, with Sparky following. In the ensuing chaos, Sparky short-circuits Gantu's ship, causing it to crash near a waterfall on Kauai. Gantu becomes stranded with 625 as a result, much to his dismay.
In Lilo & Stitch: The Series, Gantu's crashed ship remains stranded on Kauai. However, his ship contains an experiment analyzer that announces when an experiment is activated, and informs of its number and function. It also shows a 3-D image of the experiment activated for further recognition. When this happens, Gantu leaves his ship in an attempt to capture the experiment. So far, he has successfully captured several of the experiments that Lilo was unable to herself. However, in "Snafu", Lilo, Stitch, and a few of Stitch's cousins manage to break into Gantu's ship and free all the captive experiments.
Side Note: It should also be noted that the ship Gantu flew during the events of the TV series looks very different than the one he had flown in the original film, particularly the fact that it is now much larger, has a smaller cockpit, and an extra thruster. This may have been due the fact that his first ship was destroyed by Stitch at the end of the first film after he freed Lilo and tossed Gantu out of the cockpit, and was either rebuilt, upgraded and/or replaced.
In Leroy & Stitch, Gantu leaves 625 (later known as Reuben) alone on his now junkyard ship, and takes the two-man shuttle to break Hämsterviel out of prison and redeem himself. Later, Lilo goes over to Gantu's ship and asks 625 to use the videophone so she could talk to Stitch, who had gone into space to recapture Hämsterviel, and even makes a sandwich as a peace offering. Reuben initially denies being that he's too busy turning the ship into a sandwich shop, but eventually complies. After the call, Lilo finds out that the Stitch aboard the BRB is actually an imposter. She asks Reuben for help in saving Stitch, but he claims it's not their problem. Lilo then enlightens Reuben on how he could do whatever Stitch can, prompting him to reveal his incredible powers and fix the ship to make it fully operational again. The two then fly the ship to Turo to warn the Grand Councilwoman, only to discover that they were too late.