The existing medium access control (MAC) protocol of Wi-Fi networks (i.e., carrier-sense multiple access with collision avoidance (CSMA/CA)) suffers from poor performance in dense deployments due to the increasing number of collisions and long average backoff time in such scenarios. To tackle this issue, we propose an intelligent wireless MAC protocol based on deep learning (DL), referred to as DL-MAC, which significantly improves the spectrum efficiency of Wi-Fi networks. The goal of DL-MAC is to enable not only intelligent channel access but also intelligent rate adaptation. To achieve this goal, we design a deep neural network (DNN) that takes the historical received signal strength indications (RSSIs) as inputs and outputs joint channel access and rate adaptation decision. Notably, the proposed DL-MAC takes the constraints of practical applications into account and the DL-MAC is evaluated using the real wireless data sampled from the actual environments on the 2.4GHz frequency band. The experimental results show that our DL-MAC can achieve around 86\% performance of the global optimal MAC, and around the double performance of the traditional Wi-Fi MAC in the environments of our lab and the Shenzhen Baoan International Airport departure hall.