This paper presents a two-stage approach that is effective for performing fast clustering. First, a competitive neural network (CNN) that can harmonize mean squared error and information entropy criteria is employed to exploit the substructure in the input data by identifying the local density centers. A Gravitation neural network (GNN) then takes the locations of these centers as initial weight vectors and undergoes an unsupervised update process to group the centers into clusters. Each node (called gravi-node) in the GNN is associated with a finite attraction radius and would be attracted to a nearby centroid simultaneously during the update process, creating the Gravitation-like behavior without incurring complicated computations. This update process iterates until convergence and the converged centroid corresponds to a cluster. Compared to other clustering methods, the proposed clustering scheme is free of initialization problem and does not need to pre-specify the number of clusters. The two-stage approach is computationally efficient and has great flexibility in implementation. A fully parallel hardware implementation is very possible.