The electronic structure of an isostructural series of molecular conductors, beta'-X[Pd(dmit)(2)](2), is systematically studied by a first-principles method based on the density-functional theory. The calculated band structures are fitted to the tight-binding model based on Pd(dmit)(2) dimers on the triangular lattice. We find a systematic variation in the anisotropy of the transfer integrals along the three directions of the triangular lattice taking different values. The transfer integral along the face-to-face stacking direction of Pd(dmit)(2) dimers is always the largest. Around the quantum spin liquid, X = EtMe3Sb, the other two transfer integrals become comparable. We also report sensible differences in the distribution of wavefunctions near the Fermi level between the two dmit ligands of the Pd(dmit)(2) molecule.