Abstract Clustering is a useful data mining technique which groups data points such that the points within a single group have similar characteristics, while the points in different groups are dissimilar. Density-based clustering algorithms such as DBSCAN and OPTICS are one kind of widely used clustering algorithms. As there is an increasing trend of applications to deal with vast amounts of data, clustering such big data is a challenging problem. Recently, parallelizing clustering algorithms on a large cluster of commodity machines using the MapReduce framework have received a lot of attention. In this paper, we first propose the new density-based clustering algorithm, called DBCURE, which is robust to find clusters with varying densities and suitable for parallelizing the algorithm with MapReduce. We next develop DBCURE-MR, which is a parallelized DBCURE using MapReduce. While traditional density-based algorithms find each cluster one by one, our DBCURE-MR finds several clusters together in parallel. We prove that both DBCURE and DBCURE-MR find the clusters correctly based on the definition of density-based clusters. Our experimental results with various data sets confirm that DBCURE-MR finds clusters efficiently without being sensitive to the clusters with varying densities and scales up well with the MapReduce framework.