The present study proposes an improved Quantum-behaved particle swarm optimization algorithm based on the two-body problem model (QTPSO) for solving the problem that other quantum-behaved particle swarm optimization algorithms easily converge on local optimal solutions when solving complex nonlinear problems. In the proposed QTPSO algorithm, particles are categorised as core particles and edge particles. Once the position of the core particle is determined, the edge particle appears in the vicinity of the attractor exhibiting a high probability, and the attractor is obtained through the random weighted sum of the core particle and the optimal mean position. Through simulation of the motion of these two particles by applying the interaction of the particles in the two-body problem, this mechanism not only improves the diversity of the population, but also enhances the local search capacity. To validate the proposed algorithm, three groups of experimental results were obtained to compare the proposed algorithm with other swarm intelligence algorithms. The experimental results indicate the superiority of the QTPSO algorithm.