Dixon resultant is a fundamental tool of elimination theory. It has provided the efficient and practical solutions to some benchmark problems in a variety of applications domains, such as automated reasoning, automatic control, robotics and solid modeling. The major task of solutions is to construct the Dixon resultant matrix, the entries of which are more complicated than the entries of other resultant matrices. An existing extended recurrence formula can construct the Dixon resultant matrix fast. In this paper, we present a detailed analysis of the computational complexity of this algorithm. Parallel computation can be used to speed up the recursive procedure. Moreover, some experimental results are demonstrated by a range of nontrivial examples.