One of the major problems for attaining fusion is to heat the plasma particles to very high temperatures.High gain is essential for a fusion reactor and greater energy efficiency can reduce energy costs. Ion beam injection is one method used to heat plasma inside a fusion reactor. A fusion of deuteron with the isotope lithium-6, D6Li is more difficult than a fusion of deuterium and tritium,DT. In this paper, it is proposed to inject laser-driven deuteron beam in the fast ignition (FI) scheme for inertial confinement fusion (ICF) in the D6Li plasma. Fusion occurs as injected high-energy deuteron ions slow down in the plasma. The results show that the reaction probability increases by increasing electron temperature. The stopping power of electrons and ions decrease with the increase of temperature. When the energy of deuteron beam is achieved at a few hundred keV, stopping power of the electrons would be more than ions. Nuclear stopping power is considerable at very low deuterons energies. The deuteron beam range reduces as incident energy decreases. At low hot spot temperatures, deuterons can be deposited immediately within a very little range. The contribution of the released energy due to the deuteron beam interaction with ions into D6Li plasma provides the additional heating, which generally increases the energy efficiency. The investigations indicate that fusion energy efficiency is independent of lithium-6 numerical density, initial deuteron beam range and increases with electron temperature. The highest value of energy efficiency occurs with lower energy deuteron beam around the 2.5-MeV range from deuteron beam-target fusion.