In the bounded domain with C^1,α boundary, the existence of positive solutions for a class of quasilinear singular elliptic system was studied. For such system with three negative exponents, that is, a singular system, the traditional methods, such as the Morse theory, the theory of sub-and super-solutions and minimax methods, which are used usually to deal with semilinear elliptic systems in the past, can not be used directly. So, for this kind of quasilinear elliptic systems, sub-and super-solutions of the system were first constructed on the basis of the sub-and super-solution theory. Next, a set was defined according to the obtained sub-and super-solutions, and it was verified that in the corresponding set the defined operator satisfies the related conditions of the sufficient Schaulder fixed point theorem. Then, the positive solutions of the quasilinear singular elliptic system were obtained according to the fixed point theorem.