A multi-domain GDQ approach is presented in this paper for the analysis of various hollow conducting waveguides with rectangular boundaries. The present approach first decomposes the whole computational domain into several subdomains. Then in each sub-domain, the GDQ method is applied to discretize the derivatives in the Helmholtz equation. The resultant eigenvalue equation system is solved by the standard eigenvalue solver. It is demonstrated in this work that accurate cutoff wavenumbers can be simultaneously computed by multi-domain GDQ approach using just a few grid points. As a consequence, the required computational effort is tiny. The multi-domain GDQ results agree very well with available data in the literature. No spurious modes are found in present study.