An accurate technique to perform NURBS surface fitting via genetic algorithms is presented. In this technique, the initial NURBS surface is generated by using object points as control points. Then, the genetic algorithm computes the weights and control points to obtain the NURBS surface fitting. The genetic algorithm is implemented through an objective function, which is deduced from NURBS surface and object points. The objective function is minimised by means of simulated binary crossover. This procedure is carried out based on the initial NURBS surface and NURBS surface constructed by employing the object height average as control point. Thus, the genetic algorithm provides the weights and control points of the NURBS surface that represent the object shape. The proposed algorithm improves the accuracy and speed of the NURBS fitting, which is created via genetic algorithms and gradient methods. It is because the proposed algorithm calculates the weights and control points from a known search space, which is produced by NURBS surfaces. Thus, the genetic algorithm minimises the objective function in fast form with high accuracy. The contribution of the proposed method is corroborated by an evaluation based on accuracy and speed of the traditional genetic algorithms and gradient methods.