The Multidimensional Knapsack Problem (MKP) is a kind of typical multi-constraint combinatorial optimization problems. In order to solve this problem, a Greedy Binary Lion Swarm Optimization (GBLSO) algorithm was proposed. Firstly, with the help of binary code transform formula, the locations of lion individuals were discretized to obtain the binary lion swarm algorithm. Secondly, the inverse moving operator was introduced to update the location of lion king and redefine the locations of the lionesses and lion cubs. Thirdly, the greedy algorithm was fully utilized to make the solution feasible, so as to enhance the local search ability and speed up the convergence. Finally, Simulations on 10 typical MKP examples were carried out to compare GBLSO algorithm with Discrete binary Particle Swarm Optimization (DPSO) algorithm and Binary Bat Algorithm (BBA). The experimental results show that GBLSO algorithm is an effective new method for solving MKP and has good convergence efficiency, high optimization accuracy and good robustness in solving MKP.