This paper presents the extension of the global description approach of a discontinuous function, which is proposed in the previous paper, to a spectral domain decomposition method. This multi-domain spectral immersed interface method(IIM) divides the whole computation domain into the smooth and discontinuous parts. Fewer points on the smooth domains are used via taking advantage of the high accuracy property of the spectral method, but more points on the discontinuous domains are employed to enhance the resolution of the calculation. Two discontinuous problems are tested to verify the present method. The results show that the domain decomposition technique can reduce the error of the spectral IIM, especially when more collocation points are placed around the discontinuity. The present method is favorable for the reason that the same level of the accuracy can be reached, in spite of the enlarged computational domain. This paper presents the extension of the global description approach of a discontinuous function, which is proposed in the previous paper, to a spectral domain decomposition method. This multi-domain spectral immersed interface method (IIM) divides the whole computation domain into the smooth and discontinuous parts. Fewer points on the smooth domains are used via taking advantage of the high accuracy property of the spectral method, but more points on the discontinuous domains are employed to enhance the resolution of the calculation. Two discontinuous problems are tes to verify the present method. The results show that the domain decomposition technique can reduce the error of the spectral IIM, especially when more collocation points are placed around the discontinuity. The present method is favorable for the reason that the same level of the accuracy can be reached, in spite of the enlarged computational domain.