Precious reversible data hiding in encrypted image (RDH-EI) methods vacate room for data embedding in encrypted version. However, the requirement of reversible data embedding of the content owner is ignored. This paper proposes a new framework for RDH-EI using generalized reversible contrast mapping (GRCM), which vacates room for data embedding in the encrypted image. Meanwhile, some secret data is also embedded in the image before encryption by the content owner. After image encryption and update, it is easy for the remote server to reversibly embed data into the encrypted image. The proposed method guarantees the reversibility, i.e., the embedded data can be exactly extracted and the original image be perfectly recovered after decryption. Experimental results also indicate the effectiveness of the proposed method.