In this study, an innovative parallel finite volume projection algorithm with a novel red-black coloring approach is proposed to solve the two-phase flow control equations using the phase field method. This strategy relies on the explicit advancement of the pressure Poisson equation, thus effectively overcoming the efficiency limitation inherent in the traditional projection algorithms for solving the incompressible Navier-Stokes equations. Moreover, we implement an interleaved scanning strategy for updating nodal variables, which significantly enhances the spatiotemporal coupling in a compact manner. The integration of this technique with the phase field method facilitates more accurate capture of interface dynamics and topology at a lower cost. Test results show that, utilizing a grid size of 131 072 and an 8-thread CPU parallelization, the proposed parallel algorithm is more than 80 times more efficient than the serial standard projection algorithm.