This paper proposes a coevolving Memetic clustering algorithm namely CoMCA for simultaneous partitional clustering and feature weighting. Particularly, CoMCA uses a coevolving particle swarm optimization (PSO) with two swarms for the global search of optimal combination of cluster centroids and feature weights. In each iteration of PSO, a local search based on K-means and gradient descent is introduced to fine-tune the best solution. Comparison study of CoMCA to K-means, PSO clustering, Fuzzy C-means, and WK-Means on test data demonstrates that CoMCA is robust in highlighting relevant features and attaining better (or competitive) performance than the other counterpart algorithms in terms of inter-cluster variance and Rand Index.