This paper proposed a random sigma-delta modulator(RSDM), which is constructed by a 1st order sigma-delta modulator(SDM) and a simple structured random binary generator(RBG). The 1st order SDM produces a switching pulse waveform which has the same low-frequency component as the reference input, while the RBG spreads the distribution of the number of sampling per switching cycle, and thus disperses the spectrum spikes in the output. The relationship between the harmonic spectra and the number of sampling per switching cycle is studied through computer simulations, and the frequency spectra of the RSDM are confirmed in an experimental setup.