Fractional order particle swarm optimization (FOPSO) is an improved particle swarm optimization algorithm with trajectories memory. In the multimodal constrained optimization problem, a neighborhood adaptive constrained fractional order particle swarm optimization (NAFPSO) method was proposed to solve the problem that FOPSO was easy to premature and sensitive to the initial parameters. In the algorithm, the positions and velocities of particles in the swarm were updated by the neighborhood topologies adjusted dynamically according to the evolution state of particles, so as to improve the global optimizing ability and convergence speed. Meanwhile, the penalty function with penalty factor was employed to force the particles to approach the feasible area. The differential mutation strategy was designed to increase the swarm diversity and enhance the particle ability to escape from local optimum. 9 constrained benchmarks were used to test the effectiveness and convergence performance of the proposed algorithm, and then it was applied to 2 constrained engineering design problems. Comparison analysis shows that the proposed algorithm has higher optimization ability, faster convergence, higher accuracy and better stability, and can be applied to solve complex constrained engineering design optimization problems effectively.