Grey wolf optimizer (GWO) algorithm is a swarm intelligence optimization technique that is recently developed to mimic the hunting behavior and leadership hierarchy of grey wolves in nature. It has been successfully applied to many real world applications. In the GWO algorithm, “C”is an important parameter which favoring exploration. At present, the researchers are few study the parameter “C”in GWO algorithm. In addition, during the evolution process, the other individuals in the population move towards to the α, β, and δ wolves which are to accelerate convergence. However, GWO is easy to trap in the local optima. This paper presents a modified parameter “C”strategy to balance between exploration and exploitation of GWO. Simultaneously, a new random opposition-based learning strategy is proposed to help the population jump out of the local optima. The experiments on 23 widely used benchmark test functions with various features, 30 benchmark problems from IEEE CEC 2014 Special Session, and three engineering design optimization problems. The results reveal that the proposed algorithm shows better or at least competitive performance against other compared algorithms on not only global optimization but also engineering design optimization problems.