A well-known pressure correction method, a SIMPLE algorithm, is extended to treat compressible flows. Collocated grids are used and density is linked to pressure via an equation of state. The influence of pressure on density in the case of compressible flows is implicitly incorporated into the extended SIMPLE algorithm. The first-order Upwind and high-order Quick scheme are compared with respect to an accuracy and convergence time at all speeds. The extended method is verified on a number of test cases and the results are compared with other numerical results available in the literature. The calculated results show that the Quick scheme improves accuracy at all speed and also reduces the calculation time at supersonic flows, compared with the Upwind scheme.