We study the Kitaev-Heisenberg model on a triangular lattice by using the two-dimensional density-matrix renormalization group method. Calculating the ground-state energy and spin structure factors, we obtain a ground-state phase diagram of the Kitaev-Heisenberg model. As suggested by previous studies, we find a 120 degrees antiferromagnetic (AFM) phase, a Z(2)-vortex crystal phase, a nematic phase, a dual Z(2)-vortex crystal phase (the dual counterpart of the Z(2)-vortex crystal phase), a Z(6) ferromagnetic phase, and a dual ferromagnetic phase (the dual counterpart of the Z(6) ferromagnetic phase). Spin correlations discontinuously change at phase boundaries because of first-order phase transitions. We also study the relation among the von Neumann entanglement entropy, entanglement spectrum, and phase transitions of the model. We find that the Schmidt gap closes at phase boundaries and thus the entanglement entropy clearly changes as well. This is different from the Kitaev-Heisenberg model on a honeycomb lattice, where the Schmidt gap and entanglement entropy are not necessarily a good measure of phase transitions.