A mutual password authentication scheme which makes use of discrete logarithm problem (DLP) in finite fields to encrypt messages and takes USB token and password as the two authentication factors to enhance security is proposed in this paper. Meanwhile, a secure cloud storage access model which applies and verifies the good performance of the proposed scheme is introduced. In addition, some criteria of the USB token-based password authentication is summarized from previous works and is used to check the security and functionality of the proposed scheme through detailed cryptanalysis. Furthermore, comparison from theoretical analysis and experimental results with other related authentication schemes shows that the proposed scheme is feasible to cloud storage with high efficiency.