The median and/or paired fin (MPF) swimming mode of fish has extremely strong maneuverability, which is urgently needed for unmanned underwater vehicles. To fill the research gap in the entire autonomous swimming process in MPF swimming mode under self-propulsion, a numerical solution method for three degree-of-freedoms self-propelled swimming of biomimetic robotic fish (BRF) coupled with fluid dynamics and body dynamics were established. A Computational Fluid Dynamics (CFD) model was developed to simulate three-degree-of-freedom autonomous swimming in a bionic robotic fish propelled by dual undulating fins. Hydrodynamic performance was systematically investigated through parameters including locomotion velocity, pressure distribution, and power expenditure during rectilinear swimming. Variations in undulation frequency f and wavelength λ were examined. Results demonstrated that the longer the wavelength and the higher the wave frequency, the greater the propulsion speed of the bionic fish, the greater the propulsion force, and the greater the power consumed. The research results reveal the self-propulsion swimming characteristics of bionic robotic fish, laying a theoretical foundation for the development of highly maneuverable robotic fish.