Numerical simulation of a flow past an undulating two-dimensional fish-like body is carried out by using Lattice Boltzmann Method (LBM) and our newly-proposed Immersed Boundary Velocity Correction Method (IBVCM). The fish body used in the simulation is constructed from the NACA0012 airfoil. Based on the kinematics for undulatory swimming fish, the midline of the fish-like body oscillates transversally in the form of traveling wave. The current study is focused on the effects of Reynolds number and the character of midline oscillation on the generation of propulsion force. The investigation indicates that the higher Reynolds number, or higher frequency, or higher amplitude of midline oscillation produces a higher propulsion force. Among the parameters affecting the generation of propulsion force, the amplitude of midline oscillation is the most noticeable factor.