The simulation of injection molding involves the filling of cavities and runners in complicated shapes. The 3D elements in large numbers are generally required to satisfy the precise simulation of real processes. It results in the computation in large scales, so that the efficiency of computation becomes very important. On the basis of previous explicit software realized by the authors, the new algorithm avoids the global solution for pressure fields to improve its efficiency. Another feature of the new algorithm is the use of same order interpolation elements instead of MINI elements, which simplifies significantly the software procedures. Except for the operations at element level, neither global solution nor the construction of global matrix is required in simulation. A special feedback regulation strategy is used to meet the incompressibility in filled domain at each time step. In case of the mold filling problems, this method provides a fast way to simulate the filling processes. The computational cost is about linearly proportional to the degree of freedom number. Comparison of velocity field obtained by the previous algorithm using MINI element and analytical theoretical solution proves that the feedback regulation strategy in the new algorithm can satisfy well incompressibility. Moreover, comparison with the results of filling process and temperature field obtained by the previous algorithm proves the validity of the new algorithm. POLYM. ENG. SCI., 49:1243-1252, 2009. (C) 2009 Society of Plastics Engineers