Limited to the calculation capability of computers and computational cost, some physical assumptions for flows are needed in the realistic simulation, such as inviscid flow, incompressible flow and so on, which will take various degrees of error in the simulation results. To solve this problem, a numerical method used to solve the weak compressible viscous flow is presented here that is capable to solve the weak compressible viscous flow whether there is a static or moving solid body in the flow field. Starting from the state equation of water, the velocity and pressure governing equations for weak compressible viscous flows are derived rigorously. Considering the effect of solid body, the Boundary Data Immersion Method (BDIM), which can accurately represent moving bodies in flow and underwater acoustic simulations, is employed to couple the fluid sub-domain and solid sub-domain. Therefore, the flow field with the effects of the compression and viscosity is solved by coupling the weak compressible viscous flow and the BDIM. The effectiveness and accuracy of our method are validated by three two dimensional cases, and the results indicate that the novel method simulates the flow flied accurately and effectively for both a static and moving solid body.