In this paper, a deep neural network (DNN) model is proposed for the behavioral modeling of nonlinear power amplifiers with supply dependency. Although the conventional nonlinear model, such as the Volterra series, has high accuracy, it is not commonly implemented because of its complexity. However, with manageable complexity, the multidimensional input parameters of the proposed model ensure the modeling of the nonlinear behavior of power amplifiers with supply voltage dependency. The proposed model is trained by multi-tone signals on a 10-W power amplifier and validated by comparing the output spectrum and the third-order intermodulation (IMD3) of the model versus the measured data. The output spectrum shows less than 0.38 dB of error over a bandwidth of 10 MHz and input power from 11 dBm to 17 dBm, and the IMD3 error is less than 0.1 dB over the output power range.