The stochastic resonance(SR)in a time-delayed bistable system driven by square-wave signal under the action of multiplicative and additive colored noise and additive asymmetric dichotomous noise is studied. Based on the small delay-time approximation, the expression of the output signal-to-noise ratio(SNR)of this system is derived under the adiabatic approximation condition. The analysis results shows that the SNR exhibits SR behavior with the change of the intensity and asymmetry of the dichotomous noise, the amplitude of the square-wave signal, and the intensity of the multiplicative and additive colored noise.The SNR varies non-monotonously with the delayed-time, correlation time of colored noises, and system parameters.