Quantum-behaved particle swarm optimization (QPSO) has shown to be an effective algorithm for solving global optimization problems that are of high complexity. This paper presents a new QPSO algorithm, denoted LI-QPSO, which employs a model-based linear interpolation method to strengthen the local search ability and improve the precision and convergence performance of the QPSO algorithm. In LI-QPSO, linear interpolation is used to approximate the objective function around a pre-chosen point with high quality in the search space. Then, local search is used to generate a promising trial point around this pre-chosen point, which is then used to update the worst personal best point in the swarm. Experimental results show that the proposed algorithm provides some significant improvements in performance on the tested problems.