Cloud computing promises users massive scale outsourced data storage services with much lower costs than traditional methods. However, privacy concerns compel sensitive data to be stored on the cloud server in an encrypted form. This posts a great challenge for effectively utilizing cloud data, such as executing common SQL queries. A variety of searchable encryption techniques have been proposed to solve this issue; yet efficiency and scalability are still the two main obstacles for their adoptions in real-world datasets, which are multi-dimensional in general. In this paper, we propose a tree-based public-key Multi-Dimensional Range Searchable Encryption (MDRSE) to overcome the above limitations. Specifically, we first formally define the leakage function and security of a tree-based MDRSE. Then, by leveraging an existing predicate encryption in a novel way, our tree-based MDRSE efficiently indexes and searches over encrypted cloud data with multi-dimensional tree structures (i.e., R-trees). Moreover, our scheme is able to protect single-dimensional privacy while previous efficient solutions fail to achieve. Our scheme is selectively secure, and through extensive experimental evaluation on a large-scale real-world dataset, we show the efficiency and scalability of our scheme.