Brief bursts of high frequency (HF) and very high frequency (VHF) radio emissions unaccompanied by strong low frequency radiation have been observed during initiation and propagation of lightning or thunderstorm electrical breakdown without leading to fully-fledged lightning. This paper investigates a physical mechanism to generate such radio bursts by electrical discharge activity inside a thundercloud. When a discharge consists of many high frequency emission sources, such as streamers, that generate currents in random directions, its radiation spectrum peaks in the HF and VHF bands, and the spectral magnitudes in low frequencies are much smaller or even negligible. Combined with recent observational findings, the present study suggests that lightning initiation may begin with a short burst of many randomly occurring small-scale discharges in a localized thundercloud region.