With the rapid development of cloud computing paradigm, data owners have the opportunity to outsource their databases and management tasks to the cloud. Due to the privacy concerns, it is required for them to encrypt the databases before outsourcing. However, there is no existing techniques handling range queries in a fully secure way. Therefore, in this paper we focus exactly on secure processing of range queries over outsourced encrypted databases. To efficiently process secure range queries, the extraordinarily challenging task is how to perform fully secure range queries over encrypted data without the cloud ever decrypting the data. To address the challenge, we first propose a basic secure range queries algorithm which is not absolutely secure (i.e., leaking the privacy of access patterns and path patterns). To meet a better security, we present a fully secure algorithm that preserves the privacy of the data, query, result, access patterns and path patterns. At last, we empirically analyze and conduct a comprehensive performance evaluation using real dataset to validate our ideas and the proposed secure algorithms.