A velocity-coefficient independent pressure correction equation is proposed based on a modified SIMPLE algorithm for the solution of incompressible Navier-Stokes equations. In the conventional approach of SIMPLE, the central velocity coefficient of linearized momentum equation updates with every non-linear iteration within a time step. Since the pressure correction equation is coupled to the velocity coefficient term the pressure matrix coefficients obtained from the discretized pressure Poisson’s equation also get updated. As a consequence, the preconditioning step used to accelerate the convergence of pressure linear system becomes computationally expensive as the preconditioner is computed at every SIMPLE iteration. In the proposed approach this difficulty is circumvented wherein the velocity coefficient term in the pressure correction equation is repositioned with the velocity term such that the pressure matrix coefficients no longer depend on the same. Hence the preconditioner is computed only once at the first non-linear iteration that is stored and re-used for the subsequent iterations thereby reducing the overall CPU time of simulation. © 2023 Taylor & Francis Group, LLC.