Abstract Soft robotic fish has a lot of benefits. This paper aims to create a robotic fish with a soft pectoral caudal fin which was powered by IPMC material. The soft robotic fish’s hydrodynamic performance during straight swimming is numerically computed using the overset grid approach. Compared with the soft tail fin driven with a driving frequency of 0.05 Hz and those driven together with three soft pectoral fins with different driving frequencies and amplitude, the hydrodynamic coefficients and pressure of the bionic robotic fish are analyzed. We can find the regions of distinct positive and negative pressure during the IPMC soft caudal fin flapping. And the forward pressure component provides forward propulsion for the bionic fish. The greater the flapping frequency of the IPMC soft pectoral fin is, the smaller the amplitude is, and the greater the drag force receives. It is concluded that while the driving frequency of soft pectoral fins is 0.05 Hz, the amplitude is 5.64 mm, and the soft pectoral fin driving effect is good. Further research into how soft pectoral caudal fin frequency and amplitude affect the hydrodynamic capabilities of bionic fish was also made.