For the Plane-Gaussian (PG) artificial network, its network parameters are generated from k-plane clustering algorithm in training phase. Compared with random parameters of extreme learning machine (ELM), PG is a time-consumer and easy to trap into local optimal solution. To improve the performance of PG network, inspired by ELM in this paper, a new training method based on random projection for PG network, termed as RandPG, is proposed. Typically, for the three-layer network, the weight matrix between input and hidden layers is selected by random projection to speed training network, and the weight matrix between hidden and output layers is obtained by Moore-Penrose generalized inverse. It is proved that the network has global approximation theoretically. Meanwhile, the effectiveness of this network is tested on the line-distribute datasets, planedistribute datasets and several UCI datasets. The results indicate that RandPG provides a simple and convenient way to train parameters of neural network, and it not only follows the advantage of PG network, which is more suitable for classifying subspace-distribute datasets, but also significantly accelerates its learning speed.