The effect of anisotropy caused by a confining potential on the properties of fermionic cold atoms in a triangular optical lattice is systematically investigated by using the dynamical cluster approximation combined with the continuous time quantum Monte-Carlo algorithm. The quantum phase diagrams which reflect the temperature-interaction relation and the competition between the anisotropic parameter and the interaction are presented with full consideration of the anisotropy of the system. Our results show that the system undergoes a transition from Fermi liquid to Mott insulator when the repulsive interaction reaches a critical value. The Kondo effect also can be observed in this system and the pseudogap is suppressed at low temperatures due to the Kondo effect. A feasible experiment protocol to observe these phenomena in an anisotropic triangular optical lattice with cold atoms is proposed, in which the hopping terms are closely related to the lattice confining potential and the atomic interaction can be adjusted via the Feshbach resonance.
