Because the forming area involved in traditional reverse multistage incremental forming is only located inside the model, the sheet-metal thinning rate is relatively large. Particularly, the straight-wall parts with a narrow internal space cannot be formed using traditional multistage incremental forming. Therefore, a negative multistage incremental forming that extrudes the sheet from the forward and the reverse side of the straight-wall part is proposed in this paper. In this method, firstly, the auxiliary surface is generated to divide the straight-wall part model into three forming regions; secondly, the first- and second-stage forming are carried out from the forward side of the straight-wall part with support, respectively; Thirdly, the third-stage forming is carried out from the forward side of the straight-wall part without support. The software system for auxiliary-surface generation, the straight-wall parts partition, each intermediate-stage-forming model, and each stage-forming toolpath generation was developed by using C++, VC++, and OpenGL library. In order to verify the feasibility of the proposed method in this paper, the forming experiments of a 1060 aluminum sheet were conducted using traditional reverse multistage forming and the proposed method in this paper, and the forming effects were compared and analyzed. The results show that compared with traditional reverse multistage incremental forming with forward-side extrusion, the multistage incremental forming method with the forward and the reverse-sided extrusion proposed in this paper can increase the area of the sheet participating in the deformation and avoid the problem of excessive thinning of sheet thickness, especially suitable for the straight-wall part model with narrow internal space.