Position prediction is the basis of guiding radar to seek, capture and track space targets, although there's a risk of insufficient accuracy for narrow beam radar due to the influence of orbit determination and propagation error. Since the along-track error is the main factor that affects the accuracy of position prediction, this paper proposed a Constant Elevation Search (CES) method for narrow beam radar, based on the idea of along-track error compensation, to seek and capture transit targets. With along-track error estimation, all possible positions on a specified elevation can be observed, thus the success rate of capturing transit targets will be improved. Simulation shows that when the position prediction method fails, the CES method still works.