In this article, we consider a class of hyperbolic pseudo-differential equations with singular coefficient, set L=D,t,+A（t, x, D,x,）+1/（t,l,）B（t, x, D,x,）+C（t, x, D,x,） （1） where both A and B are one order diagonal operators system, and C is zeroth order operator. By transformation of variables with singularity, （1） can be re duced to operators system L=D,t,-λ（t, x, D,x,）+f（t, x, D,x,） （2） where If operators（2） satisfy the following conditions: 1. λ,j,（t, x, ξ） （j=1, 2, …, m） are real and λ,j,（t, x, D,x,） proper pseudo differential operators; 2. Hamilton field defined by λ,j,（t, x, ξ） determines a 1 parameter group of diffeomorphism; 3. Lagrange manifold defined by λ,j,（t, x, ξ） satisfies the following conditions of quantization: a) θ=0, where θ is the cohomology class of ξ·dx in H,1,（Λ, R）; b) 1/4α∈H,1,（Λ, Z）, i. e. o=α∈H（Λ, Z,4,）. where α is Moslov index; 4. |λ,j,-λ,k,|≥c,<,ξ,>,（c,>,0, j≠k） then there exists a unique E（t）∈B,∞,（R,t, L,o,） such that Hence we get the fundamental solutions of Cauchy problem of （1）. In addition, we discuss a class of high order equations which can be reduced to equation system and construct its fundamental solutions; coefficint here are all with singularity, but it does not propagate. The case of one equation of one order has been well discussed by M. Y. Chi in [2].