Computer tomography is widely used in many fields, and the quality of inversion algorithm is directly related to the success of tomography. In this paper, a computer tomography inversion algorithm based on BP neural network optimized by Quantum Particle Swarm Optimization(QPSO) is proposed. The weights and thresholds of BP neural network are optimized by QPSO. The trained network can better solve large sparse nonlinear equations. The simulation result show that the method is practical and efficient