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Efficient deep-water offshore wind power installation platforms with a pressurized self-elevating mat are a new type of equipment used for installing offshore wind turbines. However, the unstable internal pressure of the pressurized self-elevating mat can cause serious harm to the platform. This paper studies the pneumatic control system of the self-elevating mat to improve the precision of its pressure control. According to the pneumatic control system structure of the self-elevating mat, the pneumatic model of the self-elevating mat is established, and a conventional PID controller and fuzzy PID controller are designed and established. It can be seen via Simulink simulation that the fuzzy PID controller has a smaller adjustment time and overshoot, but its anti-interference ability is relatively weak. The membership degree and fuzzy rules of the fuzzy PID controller are optimized using a neural network algorithm, and a fuzzy neural network PID controller based on BP neural network optimization is proposed. The simulation results show that the overshoot of the optimized controller is reduced by 9.71% and the stability time is reduced by 68.9% compared with the fuzzy PID. Finally, the experiment verifies that the fuzzy neural network PID controller has a faster response speed and smaller overshoot, which improves the pressure control accuracy and robustness of the self-elevating mat and provides a scientific basis for the engineering applications of the self-elevating mat.