The influences on visibility of specular points are investigated from several properties of the spaceborne GPS-R system downward antenna in the oceanographic remote sensing, including beam center pointing, beam geometry and beam scanning manners. In particular, we firstly defined a subastral plane which has a one-to-one mapping relationship with points on the Earth in beam zone coverage; then presented a scheme to figure out beam zone coverage in this plane, and then analyzed the influences on visibility from beam center pointing, beam geometry and beam scanning manners. A configuration of beam geometry and beam scanning manners are proposed, in which the direction with larger half power beam width of the downward antenna's two main directions in the lobe pattern is vertical to the LEO satellite velocity direction in subastral plane. These research conclusions have been verified by simulation in the potential GPS-R system in the oceanographic remote sensing, based on the orbit of a LEO satellite which can be used in the future.