A numerical method for predicting viscous flows in complex geometries has been presented. Integral mass and momentum conservation equations are deploved and these are discretized into algebraic form through numerical quadrature. The physical domain is divided into a number of non-orthogonal control volumes which are isoparametrically mapped on to standard rectangular cells. Numerical integration for unsteady mementum equations is performed over such non-orthogonal cells. The explicitly advanced velocity components obtained from unsteady momentum equations may not necessarily satisfy the mass conservation condition in each cell. Compliance of the mass conservation equation and the consequent evolution of correct pressure distribution are accomplished through an iterative correction of pressure and velocity till divergence-free condition is obtained in each cell. The algorithm is applied on a few test problems, namely, lid-driven square and oblique cavities, developing flow in a rectangular channel and flow over square and circular cylinders placed in rectangular channels. The results exhibit good accuracy and justify the applicability of the algorithm.