Aiming at the shortcomings of quantum-behaved particle swarm optimization (QPSO) algorithm, an improved quantum-behaved particle swarm optimization (HQPSO) algorithm based on L$\acute{\rm e}$vy flight strategy and hybrid probability distribution is proposed. In the algorithm design aspect, L$\acute{\rm e}$vy flight strategy is used to renew the iterative formula of particle position, which enhances the local convergence precision and global exploration capability of the algorithm. Besides, considering premature in the later stage of iteration, a hybrid probability distribution combining normal distribution and exponential distribution is introduced into potential well model, which helps algorithm escape local optima in time. Furthermore, the experimental results on 16 benchmark functions show that HQPSO has better convergence and robustness than several other algorithms. Finally, when solving self-financing portfolio model, HQPSO provides comparable and superior numerical results compared with differential evolution, particle swarm optimization algorithm and quantum behaved particle swarm optimization algorithm.