Based on extended Dixon resultants, a new algorithm DR (Dixon resultants) is proposed to solve the system of multivariate polynomial equations. The basic idea of DR is to apply the extended Dixon resultants method to the system of multivariate polynomial equations, by taking x₁,x₂,…,x_n-1 as variables and x_n as parameter. The time complexity of DR technique is evaluated. It seems to be polynomial when the system is sparse and m=n, and the mixed volume is polynomial. Moreover, DR technique is compared with Buchberger’s algorithm and XL technique in this paper. It is shown that DR is far more efficient than Buchberger’s algorithm and XL when m=n. DR is a quite efficient algorithm and makes a good use of the sparsity of the sparse system. Besides its efficiency, another advantage of DR is that its complexity is easy to determine.