A numerical study on the flow over a square cylinder in the vicinity of a wall is conducted for different Couette-Poiseuille-based non-uniform flow with the non-dimensional pressure gradient P varying from 0 to 5. The nondimensional gap ratio L (=H /a ) is changed from 0.1 to 2, where H is gap height between the cylinder and wall, and a is the cylinder width. The governing equations are solved numerically through finite volume method based on SIMPLE algorithm on a staggered grid system. Both P and L have a substantial influence on the flow structure, time-mean drag coefficient CD, fluctuating (rms) lift coefficient (C′L), and Strouhal number St. The changes in P and L leads to four distinct flow regimes (I, II, III and IV). Following the flow structure change, the CD , C′L, and St all vary greatly with the change in L and/or P. The CD and C′L both grow with increasing P and/or L. The St increases with P for a given L, being less sensitive to L for a smaller P (< 2) and more sensitive to L for a larger P (> 2). A strong relationship is observed between the flow regimes and the values of CD , CL and St. An increase in P affects the pressure distribution more on the top surface than on bottom surface while an increase in L does the opposite. © 2018 Techno-Press, Ltd.