The molecular noise in the gene regulation network of biological clock in Drosophila was studied. Especially, we investigated the effect of molecular noise on the circadian rhythmic oscillation when the system is in the steady state region but only slightly away from the oscillating region. We show that (i) Though the prodution and the decay of the protein are stochastic with the stochastic time interval, the obvious circadian oscillation can be induced depending on the system intrinsic regulation mechanism. (ii) The coherence of molecular noise-induced oscillation is optimal under an appropriate molecular noise level, leading to the occurrence of coherence resonance.