One-way hash chains are important cryptographic primitives and have been used as building blocks of various cryptographic applications. Advantages of one-way hash chains are their simplicity and efficiency for generation based on low-powered processors with short time. However, a drawback of one-way hash chains is their difficulty of control to compute interval values of one-way hash chains. That is, when hash values in one-way hash chain are used as encryption keys, if one hash value is compromised, then the attacker can compute other encryption keys from the compromised hash value. Therefore, direct use of one-way hash chains as encryption keys is limited to many cryptographic applications, such as pay per view system and DRM system. In this paper, we propose a new concept which is called interval hash chain using a hash function. In particular, proposed hash chains are made for only computing interval hash values by using two different one-way hash chains. The proposed scheme can be applied to contents encryption scheme for grading and partially usable contents in DRM system.