The electric field on the wall of a circular chamber produced by an annular beam is compared with that of a pencil beam located at the same axes. It is proved that Beam Position Monitor (BPM) system can be used for position measurement of annular beams. Taking a single-point non-uniform model, the influence of the azimuthally non-uniformity on measurement accuracy is analyzed. And it is revealed that 10% single-point non-uniformity caused a 0.1 mm measurement deviation. A BPM system is preliminarily designed, and the radius of the button electrode as well as the radius of the output port is optimized.