This paper investigates the stochastic resonance (SR) phenomenon in an asymmetric system with coupling between multiplicative and additive noise when the coupling between two noise terms is coloured.The approximate expression of signal-to-noise ratio has been obtained by applying the two-state theory and SR exhibits in the bistable system.Moreover,the potential asymmetry γ and cross-correlation strength λ can weaken the SR phenomenon,while the cross-correlation time γ can strengthen the SR phenomenon.