An efficient approach to the fully relativistic density-functional theory (DFT) is proposed to accelerate Dirac-Kohn-Sham calculation that uses high-quality basis sets and hybrid exchange-correlation functional. The dual-level approach proposed by Nakajima and Hirao underlies the present method, estimating high-level four-component DFT energy perturbatively from reference density matrix, which is determined by a relatively inexpensive self-consistent calculation using low-quality basis sets and low-cost functional. A further approximation based on Infinite-Order Two-Component relativistic Hamiltonian is incorporated into the low-level treatment. Accuracy and efficiency were examined by benchmark calculation of spectroscopic values for MH, M-2 (M = Cu, Ag, and Au), and AtH. (C) 2011 Elsevier B.V. All rights reserved.