Solution of large scale linear programming problems is of fundamental importance in optimal resource allocation. The Simplex Method that is primarily used to solve linear programming problems computes the optimal solution in finitely many steps. However the number of steps required by the Simplex Method is not fixed and can be very large since the number of corners of the feasible set that will be visited cannot be predicted in advance. Hence the worst case complexity is exponential. Biologically inspired Particle Swarm Optimization (PSO) algorithm has been successfully used to solve a wide variety of difficult optimization problems and demonstrated to outperform other algorithms like Genetic Algorithms. In this paper hybrid PSO algorithms like Nelder-Mead Particle Swarm Optimization (NMPSO) and Gradient Particle Swarm Optimization(GPSO) have been applied to solve Linear Programming Problems. A new projection operator is introduced in this paper to project vectors with negative components into the feasible set since solutions with negative components are not feasible solutions. Performance of the hybrid PSOs and classical PSO are compared using benchmark linear programming problems. © Research India Publications.