Aiming at the capacity P-median problem of continuous domains under the dense demand, the Centroidal Capacity Constrained Power Diagram (CCCPD) theory was proposed to approximately model the continuous P-median problem and accelerate the solving process. The Power diagram was constructed by extended Balzer's method, centroid restriction was imposed to satisfy the requirements of P-median, and capacity constraint was imposed to meet the capacity requirements of certain demand densities. The experimental results show that the proposed algorithm can quickly obtain an approximate feasible solution, having the advantages of better computing efficiency and capacity accuracy compared to Alper Murata's method and Centroidal Capacity Constrained Voronoi Tessellation (CCCVT) respectively. Additionally, the proposed method has excellent adaptability to complex density functions.