Different from the existing synchronization clustering algorithm(Sync) which is recently proposed based on Kuramoto model in physics, and referring to gravitational law, a novel clustering algorithm, called large sample clustering by gravitational synchronization(LSCGS) is proposed for large datasets. Firstly, a large scale dataset is condensed into its reduced dataset by using the reduced set density estimator method. Then, the obtained reduced dataset is clustered by using the proposed gravitational synchronization clustering model with Davies-Bouldin clustering criterion to find out the most suitable clustering results. Finally, the remaining samples in the large dataset are clustered. The proposed method can detect clusters in data of arbitrary shapes, sizes and numbers without any data distribution assumptions. Extensive experiments on the large synthetic dataset, UCI real-world datasets and image segmentations indicate that LSCGS can effectively detect the clusters of the arbitrary shape, and the proposed method achieves high clustering accuracy with lower execution time.