The grey wolf optimizer (GWO) is a novel type of swarm intelligence optimization algorithm. An improved grey wolf optimizer (IGWO) with evolution and elimination mechanism was proposed so as to achieve the proper compromise between exploration and exploitation, further accelerate the convergence and increase the optimization accuracy of GWO. The biological evolution and the "survival of the fittest" (SOF) principle of biological updating of nature are added to the basic wolf algorithm. The differential evolution (DE) is adopted as the evolutionary pattern of wolves. The wolf pack is updated according to the SOF principle so as to make the algorithm not fall into the local optimum. That is, after each iteration of the algorithm sort the fitness value that corresponds to each wolf by ascending order, and then eliminate R wolves with worst fitness value, meanwhile randomly generate wolves equal to the number of eliminated wolves. Finally, 12 typical benchmark functions are used to carry out simulation experiments with GWO with differential evolution (DGWO), GWO algorithm with SOF mechanism (SGWO), IGWO, DE algorithm, particle swarm algorithm (PSO), artificial bee colony (ABC) algorithm and cuckoo search (CS) algorithm. Experimental results show that IGWO obtains the better convergence velocity and optimization accuracy.