The compound eye of insects has many excellent characteristics. Directional navigation is one of the important features of compound eye, which is able to quickly and accurately determine the orientation of an objects. Therefore, bionic curved compound eye have great potential in detecting the orientation of the target. However, there is a serious non-linear relationship between the orientation of the target and the image obtained by the curved compound eye in wide field of view (FOV), and an effective model has not been established to detect the orientation of target. In this paper, a method for detecting the orientation of the target is proposed, which combines a virtual cylinder target with a neural network. To verify the feasibility of the method, a fiber-optic compound eye that is inspired by the structure of the bee's compound eye and that fully utilizes the transmission characteristics and flexibility of optical fibers is developed. A verification experiment shows that the proposed method is able to realize quantitative detection of orientations using a prototype of the fiber-optic compound eye. The average errors between the ground truth and the predicted values of the horizontal and elevation angles of a target are 0.5951 ° and 0.6748°, respectively. This approach has great potential for target tracking, obstacle avoidance by unmanned aerial vehicles, and directional navigation control.