This paper deals with the problem of synthesis of the 3-dimensional Grasp Planning. In previous studies the genetic algorithm has been used to find optimal grasping points, but it had a limitation such as the determination time of grasping points was so long. To overcome this limitation we proposed a new algorithm which employs the Neural Network. In the Neural network we chose input parameters based on the shape of the object and output parameters resulted from optimization with the GA method. In this study the GRNN method is employed, it has been trained by the result value of optimization method and it has been tested by known object. The algorithm is verified by computer simulation.