MapReduce is considered as the de facto framework for storing and processing massive data due to its fascinating features: simplicity, flexibility, fault tolerance and scalability. However, since the MapReduce framework does not provide an efficient access method to data (i.e., an index), whole data should be retrieved even though a user wants to access a small portion of data. Thus, in this paper, we devise an efficient algorithm constructing quadtrees with MapReduce. Our proposed algorithms reduce the index construction time by utilizing a sampling technique to partition a data set. To improve the query performance, we extend the quadtree construction algorithm in which the adjacent nodes of a quadtree are integrated when the number of points located in the nodes is less than the predefined threshold. Furthermore, we present an effective algorithm for incremental update. Our experimental results show the efficiency of our proposed algorithms in diverse environments.