The background count rate of a 1-cm(3) quartz gas proportional counter (GPC) was investigated for measuring natural radioactivity levels of small samples. Using a new multiparameter digital counting system, spurious or afterpulses that contribute to background were identified by their pulse waveform and by a special event indicator defined by the time (<2000micros) between two successive pulses. With the GPC in coincidence with a low-background NaI(Tl) scintillation guard detector, the weighted mean and standard uncertainty anticoincidence counts per day (d(-1)) was 6.2+/-0.4d(-1).