Many problems in science and engineering such as biology, chemistry, computer vision, robotics, and so on, can be reduced to solve a parametric polynomial system. Such a system has two different unknowns: variables and parameters. Solving parametric polynomial system, which is the main purpose of this thesis, means finding the values of variables w.r.t. the different values of parameters. In the other words, the main obstacle in solving such a system is to describe the structure of the solution set in dependence of the parameters. In this thesis, we reduce the space of computations to the space of parameters. Then by cylindrical algebraic decomposition (CAD) method, which had been discovered by Collins, we decompose whole the space of parameters into the cells on which the initial polynomial system has constant sign. But this method requires too much computation time and its complexity is doubly exponential. Lazard and Rouillier, by introducing the concept of minimal discriminant variety, have reduced the space of computations to the parameter space and then they have used CAD to decompose the space of parameters into the cells. In this thesis, as a new result, we modify Lazard-Rouillier algorithm to compute minimal discriminant variety, and we show that with our improvements the output of our algorithm is (despite of Lazard-Rouillier algorithm) always minimal and it does not need to compute the radical of ideals.