For the channel access and resource allocation problem in the p-persistent Mobile Ad hoc NETwork （MANET）， an adaptive channel access and resource allocation algorithm with low complexity was proposed. Firstly， considering the characteristics of MANET， the optimization problem was formulated to maximize the channel utility of each node. Secondly， the formulated problem was then transformed into a Markov decision process and the state， action， as well as the reward function were defined. Finally， the network parameters were trained based on policy gradient to optimize the competition probability， priority growth factor， and the number of communication nodes. Simulation experiment results indicate that the proposed algorithm can significantly improve the performance of p-persistent CSMA （Carrier Sense Multiple Access） protocol. Compared with the scheme with fixed competition probability and predefined p-value， the proposed algorithm can improve the channel utility by 45% and 17%， respectively. The proposed algorithm can also achieve higher channel utility compared to the scheme with fixed number of communication nodes when the total number of nodes is less than 35. Most importantly， with the increase of packet arrival rate， the proposed algorithm can fully utilize the channel resource to reduce the idle period of time slot.