Non-perturbative Renormalization Group (NPRG) is a powerful method to describe the critical behaviors of the physical systems. Its formalism and applications are developing; however there are some difficulties to solve its equations, analytically. Therefore we must solve them numerically. In this thesis we will introduce NPRG, and then explain numerical algorithms to solve NPRG equations. We solve them for O(N) model (N=1) and derive the fixed points and the critical exponents with the help of numerical algorithms. Existence of Gaussian and Wilson-Fisher fixed points are confirmed by our results and we get the values of 0.324, 0.62, and 1.263 respectively for the critical exponents of and 0.041 for the anomalous dimension . These values are in good agreement with other methods. These agreements encourage us to apply NPRG for other models and physical systems.
