Inductive power transfer (IPT) systems facilitate contactless power transfer between two sides and across an air-gap, through weak magnetic coupling. However, IPT systems constitute a high order resonant circuit and, as such, are difficult to design and control. Aiming at the control problems for bidirectional IPT system, a neural networks based proportional-integral-derivative (PID) control strategy is proposed in this paper. In the proposed neural PID method, the PID gains, $$K_{P}$$, $$K_{I}$$ and $$K_{D}$$ are treated as Gaussian potential function networks (GPFN) weights and they are adjusted using online learning algorithm. In this manner, the neural PID controller has more flexibility and capability than conventional PID controller with fixed gains. The convergence of the GPFN weights learning is guaranteed using Lyapunov method. Simulations are used to test the effective performance of the proposed controller.