Based on analyzing to simplex integration formula, we give its algorithm written by pseudocode, and describe the integration procedure, and illustrate the calculation algorithm of gravity centers in polyhedron with arbitrary shape. We discuss the accuracy of above algorithms through comparing the difference between theoretical and calculated results of gravity centers in regular integral region with hollow, and analyzing their difference in different edge length ratio (10-4-104). Then the adaptive characteristics of simplex integration algorithm are discussed through analyzing integral results in irregular integral region. The results show that the relative error between calculated results and theoretical results is about 10-15-10-14, and the graphics conditions have minimal impact on integral results and the impact has not systematic characteristic. In conclusion, the results of simplex integration and gravity center have high stability and accuracy.