The effects of multiplicative noise on additive noise-induced internal signal stochastic resonance（ISR）are studied in a Neurospora circadian clock system driven by external signal or not. Two cases are investigated: multiplicative noise and additive noise are independent or correlated. The results show that in the two cases, there exists a critical intensity of multiplicative noise for the additive noise-induced ISR in the system without the external signal. When a multiplicative noise with intensity smaller than the critical level is introduced，the strength of ISR can be significantly reinforced; while the ISR behaviors cannot be further enhanced when the noise with the intensity larger than the critical level is introduced. The latter implies that the Neurospora system might be robust to environmental noise and sustain the intrinsic circadian rhythms. When the external signal is injected into the system, for the case of without correlation between two noises, there exists an optimal frequency （0003 Hz） of the signal for the ISR information amplification, but for the case of with correlation between the two noises, the ISR is suppressed by the signal with any frequency. In addition, the correlation’s intensity between the two noises can also control the ISR, and there exists a proper range of correlation’s intensity for the ISR amplification.