In this letter, a resource allocation strategy based on a deep neural network (DNN) is proposed for multi-channel cognitive radio networks, where the secondary user (SU) opportunistically utilizes channels without causing excessive interference to the primary user (PU). In the proposed scheme, the allocation of transmit power in each channel for SUs is found by utilizing the newly proposed DNN model, which separately determines the overall transmit power of individual SUs and the proportion of transmit power allocated to each channel. Both the spectral efficiency (SE) of the SU and the amount of interference caused to the PU are considered in the training of the DNN model, such that the interference caused to the PUs can be properly regulated while the SE of the SU is improved. Through simulations, we show that our scheme enables a high SE of the SU to be achieved while the interference caused to the PU can be maintained at less than the threshold.