Most of the previous haptic interfaces provides tactile feedback directly to the hand, which can impede the operability. Noting the issue, we propose a haptic system that can provide 3D vector information with continuous skin-stretch feedback. We designed the system to render a 3D vector by combining two orthogonally located continuous skin-stretch modules whose orientation could be controlled. To optimize the stimuli, we conducted a psychophysical experiment that measured human sensitivity to the orientation of the continuous skin-stretch feedback. Considering the asymmetry of tactile sensitivity, we collected the data at two locations of the forearm. The results indicate that the participants were more sensitive to the angle change when the skin-stretch feedback was aligned in the proximal-distal direction. Based on the information, we built an algorithm to set the rotation angle of the skin-stretch module to render any target 3D vector. We conducted two experiments for virtual interaction to evaluate our proposed method. In Experiment 1, we tested if adjusting the skin-stretch orientation could improve the human perception of the virtual surface features, and the result indicated a significant improvement in the surface feature perception with the orientation adjustment. Experiment 2 tested a participant's ability to follow a random 3D contour under two conditions, visual cue (V) condition, and visual and continuous skin-stretch (V+CF) cues condition. For the V+CF condition, the skin-stretch interface rendered the error 3D vector to the participant's forearm. The result indicated a significantly lower root-mean-square error for the V+CF condition than the V condition. Thus, the addition of the continuous skin-stretch feedback benefitted the participants to stay closer to the target virtual contour than with visual information only.