In this paper, the fluid flow past a square obstacle located in the center of a channel is presented using semi-implicit parallel Taylor-Galerkin finite element algorithm in two dimensions. As the flow is expected to vary most rapidly near the edges of the square obstacle, the closed graded mesh has been required in the vicinity of obstacle. For mesh convergence, different meshes are generated applying hierarchical mesh refinement technique. For different Reynolds Number (R e) values, the pressure and velocity values have been computed using the parallel algorithm. It has been observed that the wake on the downstream side of square obstacle is increased with the increase of Reynolds number. The performance of this parallel numerical scheme is measured through speed up and efficiency of distributed system. Ideal linear speed up with the number of processors has been observed. The efficiency of algorithm is increased with the use of refined mesh i.e. increasing computation overhead. Predicted results encourage solving the large problems of complex boundaries accurately and efficiently.