Stochastic multiresonance in a time-delayed asymmetric bistable system modulated by periodic rectangular signal and colored noises was investigated. By using the small time delay method and two-state theory, we have obtained the expression of its signal-to-noise ratio (SNR). The numerical results indicate the SNR exhibits stochastic multiresonance as a function of intensity of multiplicative noise, the intensity of additive noise, self-correlation time of multiplicative noise, self-correlation time of additive noise and delay time. In addition, when the SNR is a function of intensity of additive noise and delay time, the corresponding curves of SNR have four peaks.