A new artificial neural network,i.e.,polynomial feedforward artificial neural network(PFANN), which has three layers(input layer,hidden layer and output layer) is presented. The neural activation functions of hidden layer and output layer are f(x)=x p and linear function, respectively. The learning method of hidden-output layer weights is the steepest descent method and the one of input-hidden layer weights is genetic algorithm(GA) . During the learning process, the error function is decreased monotonely. So the learning algorithm is convergent and the network ,which can approximate to arbitrary continuous function , is stable. Some applying samples of PFANN, which reveales the remarkable quality, are proposed,too.