Path planning presents a key question for an autonomous robot to evolve in its environment. Hence, it has been largely dealt in recent years. Actually, finding feasible paths and optimizing them for different objectives is computationally difficult. In this context, this paper introduces a new mobile robot path planning algorithm by introducing an optimized NURBS (Non Uniform Rational B-Spline) curve modelling using Genetic Algorithm to represent the generated path from the specified start location to the desired goal. Thus, given an a priori knowledge of the environment, an accurate fitness function is used to compute a curvature-constrained and obstacles-avoiding smooth path, with minimum length and low variations of curvature. The performance of the proposed algorithm is demonstrated through extensive MATLAB simulation studies.