VANETs clustering is an emerging research topic that serves in the intelligent transportation systems of today's technology. It aims at segmenting the moving vehicles in the road environment into subgroups named clusters, with cluster heads for enabling effective and stable routing. Most of the VANETs clustering approaches are based on distributed models which make the decision of clusters creation lacking the global view of the vehicle's distribution and mobility in the environment. However, the availability of the LTE and long ranges of base station motivated researchers recently to provide center-based approaches. Unlike existing center-based clustering approaches of VANETs, this article uses the road segmenting phase named grid partitioning before providing summarized information to the clustering center. Furthermore, it presents an integrated approach as a combination of all the clustering tasks including assigning, cluster head selection, removing, and merging. Evaluation of the proposed approach named center-based evolving clustering based on grid partitioning (CEC-GP) is proven superior from the perspective of efficiency, stability, and consistency. An improvement percentage of the efficiency in (CEC-GP) over the benchmarks Center based stable clustering (CBSC) and evolving data clustering algorithm (EDCA) is 65% and 394% respectively. INDEX TERMS vehicular ad hoc networks, VANETs clustering, Center-based clustering, evolving clustering, grid based-clustering.