The detection of non-aligned double JPEG (NA-DJPEG) compression is one of the most important topics in the forensics of JPEG image. In this paper, we propose a novel feature set to detect NA-DJPEG compression based on refined intensity difference (RID), a new measure for blocking artifacts. Refined intensity difference is essentially intensity difference with compensation, which takes the negative effect of image texture into consideration when measuring blocking artifacts. The extraction pipeline of the proposed feature set mainly includes two steps. Firstly, two groups of RID histograms (totally sixteen histograms) with respect to horizontal and vertical directions are computed to describe the possible blocking artifacts in each row and column, and the bin values of these histograms are arranged to form an RID feature vector. Then, in order to make the RID feature vector less dependent on image texture and more discriminative, we calibrate it by a reference feature vector to generate a calibrated RID (C-RID) feature vector for final binary classification. Experiments have been conducted to validate the effectiveness of the C-RID feature set, and the results have shown that it outperforms the compared feature sets in most cases.