Abstract: The Groebner-Sylevester hybrid approach was presented to obtain the closed-form solutions of the direct kinematics of the Stewart mechanism robot. The reduced Groebner basis under degree lexicographic ordering for the closed-form equations was presented based on computer algebra method. And 20 Groebner basis were picked out from the 51 Groebner basis. Then a 20×20 dimensional Sylvester-s matrix was constructed, which is relatively small in size. And a 40th degree univariate equation was presented from the determinate of the matrix by analyzing the numbers of the variables in the equations. To verify the proposed algorithm, a same numerical example was calculated based on the continuation method as well as the the proposed algorithm. It shows that the proposed algorithm calculates simply and rapidly to lead to the univariate equation. The results both by using the continuation method and based on the proposed algorithm are same. Then a novel and practical algorithm to solve the direct kinematics of the parallel mechanism robot was presented.