The existing end-to-end (E2E) wireless communication systems require fewer communication modules and have a simple processing signal flow, compared to conventional wireless communication systems. However, in the absence of a differentiable channel model, it is impossible to train transmitters, used in such systems, which makes impossible to get optimal system performance. To solve this problem, an E2E wireless communication system, learned with conditional generative adversarial networks (CGANs) for channel modeling, has been proposed recently. Unfortunately, the CGAN training is prone to instability, slow convergence, and inaccurate channel modeling, which affects the system performance. To this end, a learning-based E2E wireless communication system, utilizing a deep neural network (DNN) channel module to model an unknown channel, is proposed in this paper. Simulation results show that the proposed DNN channel modeling has faster convergence, simpler network structure, and can reflect the behavior of real channels more accurately. In addition, the proposed E2E wireless communication system performs better, in terms of bit error rate (BER) and block error rate (BLER), than the E2E wireless communication system, using CGAN as unknown channel, and a traditional communication system, designed based on the prior knowledge of the channel. Compared to these two systems, at high signal-to-noise ratio (SNR) values, the proposed system can achieve a SNR gain of at least 2 dB, in communication scenarios involving frequency-selective multi-path channels.