Smith normal Form play the important role in the reduction of a multidimensional system; In this paper, we investigate the reduction of weakly linear multivariate polynomial matrix which with the determinant is the product of two distinct multivariate weakly linear polynomials;We give the sufficient and necessary conditions for such a matrix to be equivalent to its Smith normal Formal.Furthermore by the new results, we will extend an algorithm of reducing weakly linear multivariate polynomial matrices to their Smith normal forms.