In this paper, we propose a multi-channel full-duplex Medium Access Control (MAC) protocol for cognitive radio networks (MFDC-MAC). Our design exploits the fact that full-duplex (FD) secondary users (SUs) can perform spectrum sensing and access simultaneously, and we employ the randomized dynamic channel selection for load balancing among channels and the standard backoff mechanism for contention resolution on each available channel. Then, we develop a mathematical model to analyze the throughput performance of the proposed MFDC-MAC protocol. Furthermore, we study the protocol configuration optimization to maximize the network throughput where we show that this optimization can be performed in two steps, namely optimization of access and transmission parameters on each channel and optimization of channel selection probabilities of the users. Such optimization aims at achieving efficient self-interference management for FD transceivers, sensing overhead control, and load balancing among the channels. Numerical results demonstrate the impacts of different protocol parameters and the importance of parameter optimization on the throughput performance as well as the significant performance gain of the proposed design compared to traditional design.