In this work, we study the energy-efficient resource allocation problem based on chance-constrained programming for overlay cognitive orthogonal frequency division multiplexing (OFDM) system. The objective function minimizes the total power consumption and the constraint conditions include the requirement of the system outage probability and the feasibility of the subcarrier allocation solution. In order to solve the above chance-constrained resource allocation problem, two steps are taken to develop hybrid quantum particle swarm optimization (HQPSO). In the first step, we define an uncertain function according to the outage probability constraint condition and utilize the radial basis function (BRF) neural network to computer it. In the second step, HQPSO which includes quantum particle swarm optimization (QPSO) and RBF neural network is proposed. Simulation results demonstrate that the total power consumption of HQPSO is smaller than that of other algorithms while the system outage probability could be satisfied very well.