Abstract: The computational efficiency of temporal algorithms has a great influence on solving actual engineering problems with nonlinearity or numerous degrees of freedom. The explicit algorithm is one of the most effective methods to improve the efficiency. For the fluid-saturated porous media in the u -p form, the realization of the explicit-explicit algorithm depends on the diagonal mass matrix M and fluid compressibility matrix S . The accuracy and stabilization of complete algorithm also need to be considered as well. In this paper, based on the diagonalization of M and S matrices, the precise time-integration with characters of high-accuracy and stabilization was introduced to solve the fluid phase equation, and the central difference method was used to solve the solid-fluid complete dynamic equation. Consisting of the two methods, a novel efficiently explicit-explicit algorithm was proposed. A high level of stability and accuracy of the algorithm was verified by theoretical analysis and numerical examples.