In this paper, we developed a noise tolerance approach by using sigma-delta modulation, which can recover the noisy signals. Beside most of the previously schemes based on solving Single Event Upset (SEU), our approach can cope with the case of multiple faults, even the noise has been continued for a long time. The other property of our method is that no need to modify the original circuit and thus the performance of original circuit itself can be maintained. Meanwhile, an optimal Over Sampling Rate (OSR) has been proposed to obtain a minimum deviation between original and restore signals. In this experiment, we have assumed that a circuit output signal is affected by noises, and the total noise energy is about 0~50% of the original signal, then using our approach can produce a restore signal with a deviation under 2% of the original signal.