Swarm intelligence is one of the most promising area of numerical optimization to solve real‐world optimization problems. Grey wolf optimizer (GWO), which is based on leadership hierarchy of grey wolves, is one of the relatively new algorithm in the field of swarm intelligence–based algorithms. In order to solve constrained real‐world optimization problems, in this paper, a constrained version of GWO has been proposed by incorporating a simple constraint handling technique in GWO, and then an attempt is made to improve the ability of the leaders in original GWO by proposing random walk GWO (RW‐GWO) by pointing out some drawbacks in their process of searching prey. (To the best of the knowledge of the authors, a constrained version of GWO has not been developed yet. The unconstrained version of RW‐GWO has been proposed in the authors' earlier work.) The efficiency of both these proposed algorithms have been tested on the Institute of Electrical and Electronics Engineers Congress on Evolutionary Computation 2006 benchmark problems and on 3 engineering application problems to observe their comparative performance. It is concluded from the results that the proposed improved version of GWO, namely, RW‐GWO, has better potential to solve these constraint problems compared to GWO very efficiently as a constrained optimizer.