Tuna, dolphin and whale as typical thunniform mode fish have obvious differences in body size and caudal fin shape. As the main propeller, the difference in the shape of caudal fin will have a significant impact on the swimming performance of fish. In this work, numerical simulations are adopted to study the hydrodynamics of self-propelled thunniform swimming. By changing the trailing-edge profile parametrically, three different tails varying from forked tuna-like tail to the square-shaped tail are constructed. The results revealed that the tuna-like tail is most beneficial to fish long distance cruise, while the square-shaped tail is the most unfavorable. It is interesting to note that for tuna-like tail, decreasing the undulating amplitude can improve fish's long-distance cruising ability more than decreasing the pitching amplitude, but the opposite is true for the square-shaped tail. Further study on the vortex dynamics and the surface pressure distribution indicate that the backward expansion of the trailing-edge profile will delay the shedding of the leading-edge vortex and increase the existence time of low-pressure region on the caudal fin. Since the pitching angle is reduced synchronously, the delayed disappearance of the low-pressure region will generate more lateral force. This will lead to more energy loss.