A novel reversible data hiding algorithm for encrypted image based on interpolation error expansion is proposed. The proposed method is an improved version of Shiu' s. His work does not make full use of the correlation of the neighbor pixels and some additional side information is needed. The proposed method adopts the interpolation prediction method to fully exploit the pixel correlation and employ the Paillier public key encryption method. The algorithm is reversible. In the proposed method, less side information is demanded. The experiment has verified the feasibility and effectiveness of the proposed method, and the better embedding performance can be obtained, compared with some existing RDHEI-P methods. Specifically, the final embedding capacity can be up to 0.74 bpp (bit per pixel), while the peak signal-to-noise ratio (PSNR) for the marked image Lena is 35 dB. This is significantly higher than Shiu's method which is about 0.5 bpp.