This paper proposes a novel reliable neural network control (NNC) method for active vibration control of uncertain structures. First, reliable model predictive control (MPC) was established by introducing nonprobabilistic reliability constraints into traditional MPC. An importance sampling strategy was established to improve the efficiency of the entire training process to achieve sufficient accuracy. An adaptive nonprobabilistic Kalman filter was further proposed for estimating the uncertain region of system states. Compared to existing reliability-based control methods, the proposed reliable NNC ensured structural safety across broader loads. Compared with reliable MPC, reliable NNC significantly reduced the online computational load, making it suitable for vibration control of high-frequency complex structural systems. The effectiveness and superiority of the proposed reliable NNC were validated through two numerical examples and experimental verification.