Recently, Particle Swarm Optimization (PSO) algorithm has exhibited good performance across a wide range of application problems. A quick review of the literature reveals that research for solving the Quadratic Assignment Problem (QAP) using PSO approach has not much been investigated. In this paper, we design a hybrid meta-heuristic fuzzy scheme, called as variable neighborhood fuzzy particle swarm algorithm (VNPSO), based on fuzzy particle swarm optimization and variable neighborhood search to solve the QAP. In the hybrid fuzzy scheme, the representations of the position and velocity of the particles in the conventional PSO is extended from the real vectors to fuzzy matrices. A new mapping is introduced between the particles in the swarm and the problem space in an efficient way. We also attempt to theoretically prove that the variable neighborhood particle swarm algorithm converges with a probability of 1 towards the global optimal. The performance of the proposed approach is evaluated and compared with other four different algorithms. Empirical results illustrate that the approach can be applied for solving quadratic assignment problems effectively.