Abstract: The linear algebra for solving a system of linear equations has an important role in many fields of science like Engineering, Physics, Statistics and Computer Science, etc. Matrix inversion play a primary role in solving these equations. A main challenge task is to invert a large-scale matrix with several thousands or millions of rows and columns about 2n3 floating-point operations. We aimed to solve the system of linear equations based on matrix inversion in a way that achieves a high performance and reduces the time-consuming. In our research, we implement a matrix inversion on programmable Graphics Processors (GPUs) using MATLAB language for programming and Nvidia video card. The results of our method gain a higher performance than the sequential methods with simplicity of coding.