The aim of this paper is to approximate multidimensional functions feC(R) by developing a new type of Feedforward neural networks (FFNNs) which we called it Greedy ridge function neural networks (GRGFNNs). Also, we introduce a modification to the greedy algorithm which is used to train the greedy ridge function neural networks. An error bound are introduced in Sobolev space. Finally, a comparison was made between the three algorithms (modified greedy algorithm, Backpropagation algorithm and the result in (11)