Abstract: The research of Statistical Resolution Limit (SRL) based on hypothesis testing can measure the resolution ability in the statistical point and break through the Rayleigh limit. However, the researches presented have made an assumption that the amplitudes of two signals are determined, while in the reality that of the fast-fluctuating targets are random-distributed. Therefore, we derive the range statistical resolution limit of the two adjacent targets under this assumption. The studies show that both tests under two hypotheses are weighted Chi-Square distributed, and the statistical resolution performance is related to factors, such as the waveforms, the coefficients of the amplitudes and the signal-noise ratio (SNR), etc.. The simulation results demonstrate the correctness of the theoretical results, and this method accesses a much better performance compared with the MUSIC algorithm applied in the range resolution.