Power amplifier (PA) models, such as the neural network (NN) models and the multilayer NN models, have problems with high complexity. In this article, we first propose a novel behavior model for wideband PAs, using a real-valued time-delay convolutional NN (RVTDCNN). The input data of the model is sorted and arranged as a graph composed of the in-phase and quadrature ( I/Q ) components and envelope-dependent terms of current and past signals. Then, we created a predesigned filter using the convolutional layer to extract the basis functions required for the PA forward or reverse modeling. Finally, the generated rich basis functions are input into a simple, fully connected layer to build the model. Due to the weight sharing characteristics of the convolutional model's structure, the strong memory effect does not lead to a significant increase in the complexity of the model. Meanwhile, the extraction effect of the predesigned filter also reduces the training complexity of the model. The experimental results show that the performance of the RVTDCNN model is almost the same as the NN models and the multilayer NN models. Meanwhile, compared with the abovementioned models, the coefficient number and computational complexity of the RVTDCNN model are significantly reduced. This advantage is noticeable when the memory effects of the PA are increased by using wider signal bandwidths.