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An efficient method-of-moments (MoM) formulation using combined entire-domain and subdomain basis functions is proposed for simulating the resonant modes of a rectangular dielectric resonator in free space. An approximate analytical solution for the resonant mode of the DR is used as the entire-domain basis function, while a set of tetrahedral basis functions are used as subdomain basis functions. Since the main profile of the resonant mode can be well represented by the entire-domain basis function, only small number of subdomain basis functions are needed for further refinement of the representation. Compared with the MoM formulations using only subdomain or entire-domain basis functions, this method is much faster for the same accuracy. Numerical results are given and compared with other methods.