A novel block-oriented time-delay neural network (BOTDNN) model for dynamic nonlinear modeling and digital predistortion (DPD) of RF power amplifiers (PAs) is proposed. The proposed model consists of a dynamic linear network and a static nonlinear network to characterize dynamic nonlinear systems. The dynamic linear network simulates multiple linear filters using a fully connected layer with the linear activation function. The static nonlinear network is constructed based on vector decomposition and phase recovery mechanism. To validate the proposed model, experiments have been carried out with two different PAs operating at 2.4 and 39 GHz, respectively. The test results demonstrate that the proposed model has better PA modeling and nonlinear compensation capabilities than state-of-the-art PA behavioral models, while with significantly lower model complexity. Furthermore, to reduce the system cost, we investigate the problems that arise when the neural network-based behavioral models are applied to low feedback sampling rate DPD and propose an improved method. The experiments confirm that the proposed low feedback sampling rate DPD method can effectively alleviate the deterioration of linearization performance caused by undersampling.