This paper presents a new variant of Basic Particle Swarm Optimization (BPSO) algorithm named QI-PSO for solving global optimization problems. The QI-PSO algorithm makes use of a multiparent, quadratic crossover/reproduction operator defined by us in the BPSO algorithm. The proposed algorithm is compared it with BPSO and the numerical results show that QIPSO outperforms the BPSO algorithm in all the sixteen cases taken in this study.