The research for flexible structures coupling with fluid simulates and promotes the development of soft robotics. A fast and accurate numerical method is significant for a real-time simulation of robots. This research provides theoretical and critical information for experiments to reduce the possibility of failure, by anticipating the path of the underwater soft robots and the possible requiring parameters for materials. This paper researches for bio-swimming elastic rods coupling with two-dimensional incompressible Newton fluid. First, we discretize elastic rods to extensive springs and rotational springs and stablish the kinetic equations based on energy reflecting the influence of internal force on swimming rods, and solve the governing equation by leap-frog algorithm. Second, semi-Lagrangian method is used to establish a fluid solver. Finally, the simplified coupling algorithm based on immersed-boundary method is raised, calling immersed-boundary method for momentum equations. These equations update the velocity of grid near the coupling interface directly to replace the function source force play in immersed-boundary method. Combining the fluid solver, rods solver and the coupling algorithm, a integral program solving the problem of the dynamics for immersed rods numerically. Simulating the rods swimming with a referenced pose of sine curvature. Comparing the simulating result to existed experiments of filament swimming and to the swimming trajectory of soft-body fish, we find the numerical result conform to experiment result, leading to the conclusion that this algorithm and dynamic model can simulate the trajectory of discrete elastic rods swimming underwater smoothly under the influence of both internal elastic force and coupling soft body-fluid interaction. Using this program, we test several critical parameters relating to swimming performance of rods, including iteration numbers, frequency and initial phases, finding that changing the initial phase of rods will alter onward direction of elastic rods. These results prove the feasibility and possibility of this algorithm and program being used for guiding development of real soft swimmers.