Efficient sharing of the network spectrum is required to meet the exponentially growing demand of wireless communications, and the role of the medium access control (MAC) protocols has been becoming more important. In this regard, a novel MAC protocol called the renewal access protocol (RAP) was recently proposed. It was shown that the RAP achieves optimal throughput, high short-term fairness, and near-optimal delay performances when the number of nodes in the network is known to all nodes. However, it is not easy for a node to know the number of nodes in the network. So we propose an adaptive version of the RAP called the adaptive renewal access protocol (A-RAP) in this paper. A node equipped with the A-RAP estimates the number of nodes utilizing two dimensional backoff selection state, the estimated number of nodes and phase, based on its transmission results. We carefully determine two key parameters of the A-RAP, the adjustment probabilities and the numbers of phases. We also tackle the outlier problem in the A-RAP that is recently found and provide a solution to the problem. Numerical and simulation results are provided to verify that the proposed A-RAP achieves good throughput as the RAP. The results also show that the A-RAP achieves better short-term fairness than other MAC protocols proposed in the open literature.