In this paper, a SIMPLE-like algorithm on collocated grid system has been developed. The ability to suppress the spurious pressure field is achieved via introducing the pressure difference between adjacent two grid points into the convection-diffusion finite difference scheme, and the interfacial velocity is obtained by simple linear interpolation. The differencing scheme, discretization of governing equations and solution procedure of the algorithm are described in detail. In order to check the validity of the algorithm, several test cases which have analytical or benchmark solutions are presented. Good agreements are obtained between the numerical and the corresponding analytical or benchmark solutions. The ability of the improved algorithm to suppress the spurious pressure field is demonstrated via a 3-D example.