The metal foams are a promising candidate for the enhancement of heat transfer in latent heat thermal energy storage (LHTES) units. These foams can be synthesized with engineered local properties such as improved thermal conductivity or permeability in a specified direction. However, the impact of using anisotropic metal foams for thermal energy storage has not been addressed yet. In the current research, an anisotropic metal foam was modeled mathematically with engineered local properties in perpendicular directions. The solid-liquid phase transition of the copper-coconut oil LHTES unit was simulated using the finite element method. The anisotropic metal foam was defined by using an anisotropic parameter and angle. The simultaneous impact of the mounting tilt angle and the anisotropic angle of the copper foam were addressed in the phase transition behavior and charging time of the LHTES unit. The results revealed that the anisotropic angle could notably impact the thermal energy storage power. An optimum tilt angle of -45° or +45° along with a 0° anisotropic angle could lead to the maximum charging power. Thus, designing an LHTES unit using an anisotropic metal foam could save the charging about 15% (for a -45° inclination angle) and 20% (for zero inclination angle) compared to a regular metal foam. Such save in the charging time is without any penalty on the weight increase or capacity reduction for the LHTES unit.