Reversible data hiding has attracted considerable attention in recent years. Being reversible, the decoder can extract hidden data and recover the original image completely, and the difference expansion (DE) scheme can lead to a lossless pixel after secret data exacting. Furthermore, despite achieving pixel reversibility based on the concept of expanded differencing, the difference expansion scheme can cause enormous image distortion because of the size of the difference. The proposed scheme in this paper describes a novel prediction for achieving predictive error based reversible data hiding by considering the relation between a pixel and its neighboring pixel and using the predictor to identify the projected difference in pixel value. Experimental results show that the proposed scheme is capable of providing great embedding capacity without causing noticeable distortion by selecting the minimal predictor based on pixel expansion. In multilevel cases, this proposed method performs better than other existing methods. Moreover, the proposed scheme is able to pass the Chi-square test, a test used to find whether an image utilizes LSB for data hiding.