In a Gene Co-expression Network, the same or closely related genes are clustered into co-expressed groups. It is necessary to investigate the role that these genes play as far as some complex diseases like cancer are concerned in those networks. Ranking those genes actually discover the significant candidate genes for various types of cancers. There are several gene ranking algorithms proposed so far that produces the top ranked genes according to their importance with respect to a particular cancer disease. In this work, we apply multi-objective genetic algorithm, Multi-ObjectiveNetworkGA, on a gene coexpression network to find the top ranked cancer mediating genes. The algorithm is applied to publicly available real-life cancer datasets taken from NCBI (National Centre for Biotechnology Information) biological online repository. The performance of the algorithm is justified by classification using SVM classifier with linear kernel and it is compared with state-of-the-art methods on the basis of percentage of accuracy, precision, recall, and F1-Score. © 2018 IEEE.