Poisson equations are widely applied in physical and engineering problems. Most of numerical methods for solving 3D Poisson equations have no remarkable parallelism, and use the global iteration methods which limit the computational efficiency and stability. We abandon the idea of global iteration and combine the discrete sine transform theory (DST) with 27-point four-order difference scheme to modify and parallelize the 3D Poisson equation solver at the algorithm level, which separates the whole problem to several smaller independent ones and greatly improves the stability and parallel performance. For a given discrete form, common parameters can be used to solve different Possion equations so that the programming efficiency is greatly improved. The algorithm is implemented on the basis of the shared memory parallel model. Experimental results show that  for the given instance, the new algorithm has a good acceleration effect and the final error of the computing result is about 10e-5, within an acceptable rang. And the result accuracy gets improved with the increase of problem scale.