A new four-component Dirac-Kohn-Sham (DKS) method is presented. The method provides a computationally efficient way to perform fully relativistic and correlated ground state calculations on heavy-atom molecular systems with reliable accuracy. The DKS routine has been implemented in the four-component Dirac-Hartree-Fock program system REL4D. Two-component generally contracted, kinetically balanced Gaussian-type spinors (GTSs) are used as basis spinors. The one-electron and Coulomb integrals are computed analytically, and exchange-correlation potentials are calculated with a numerical grid-quadrature routine. An approximation scheme is presented to reduce the evaluation time of the two-electron repulsion integrals over full sets of small-component GTSs, (SS parallel to SS). Benchmark calculations for the ground states of the group IB hydrides, MH, and dimers, M-2 (M=Cu, Ag, and Au), by the DKS method are presented.