This paper proposes a Proximal Policy Optimization (PPO)-based adaptive channel access algorithm to address the channel access problem in Mobile Ad hoc NETwork (MANET) using p-persistent Carrier Sense Multiple Access (CSMA) protocol. An optimization problem is formulated based on the p-persistent CSMA contention model with the objective of maximizing node channel utilization. The optimization problem is modeled as a Markov Decision Process (MDP) with specifically designed states, actions, and reward functions. The PPO algorithm is employed to jointly optimize node competition probability, competition probability growth factor, and number of permitted access nodes, thereby achieving dynamic channel access strategies. Simulation results demonstrate that the proposed algorithm exhibits faster convergence than Deterministic Deep Policy Gradient (DDPG)-based solutions. In terms of channel utilization, the proposed algorithm achieves improvements of 33.3%, 48.1%, and 18.9% compared to fixed permitted-node-number schemes, fixed competition probability schemes, and preset probability schemes, respectively. It consistently outperforms other solutions in networks with up to 35 nodes. Additionally, the algorithm incorporates a service priority differentiation mechanism, enabling high-priority service nodes to achieve over 90% access success rate after convergence.