Based on the theory of SR for detecting weak signals, a novel approach of detecting the weak periodic signal using additional-signal-enhanced SR was presented. This method was analyzed with simulated signals. Through a kind of normalized scale transform, the frequency restriction condition of the signal to be detected was eliminated. The result shows that this method is simple and feasible. The weak sinusoid signal of low signal-to-noise ratio can be extracted from loud noise. The detecting approach indicates a promising prospect for mechanical fault diagnosis.