Gantry-tilted helical multi-slice computed tomography (CT) refers to the helical scanning CT system equipped with multi-row detector operating at some gantry tilting angle. Its purpose is to avoid the area which is vulnerable to the X-ray radiation. The local tomography is to reduce the total radiation dose by only scanning the region of interest for image reconstruction. In this paper we consider the scanning scheme, and incorporate the local tomography technique with the gantry-tilted helical multi-slice CT. The image degradation problem caused by gantry tilting is studied, and a new error correction method is proposed to deal with this problem in the local CT. Computer simulation shows that the proposed method can enhance the local imaging performance in terms of image sharpness and artifacts reduction.