A Doppler broadening spectrum of e

+

annihilation radiation is usually measured with a Ge (Li) solid-state detector. The background of the energy spectrum is mainly attributed by Compton sccattering of 1.28MeV γ-ray emmited from

22

Na. We have attempted to reduce the background by combining the Ge (Li) detector (136 cm

3

) with the NaI detector (

φ

40×30 mm) in coincidence. The primary results shown that background at the lower and the higher sides of 7.5keV from the peak is

respectivily

about one half and one fourth of that obtained without the coincidence and at the higher side of 12keV from the peak is eleven times less than that. It is a simple and feasible experiment and possible to decrease the background further.