Ridgelet neural network is a new model of artificial neural network. In this paper, an adaptive ridgelet neural network with one single hidden-layer is constructed by substituting the ridgelet function for the S-type activation function. To obtain higher accuracy and learning speed, a hybrid algorithm for training the network is researched based on conventional ones— particle swarm optimization and stochastic gradient descending algorithm. In one generation of the swarm, the nonlinear parameters of the network, direction u, location b and scale a, are optimized by an improved PSO algorithm— ρ -PSO and the linear ones, the weights w, are optimized by stochastic gradient descending algorithm. Two suit of experiments show that this hybrid training algorithm is more accurate and speedy than the conventional ones and ridgelet neural network is a prospective tool and direction of artificial neural network.