The fast ignition approach to ICF consists in first compressing the fuel to high density by a suitable driver and then creating the hot spot required for ignition by means of a second external pulse. If the ignition beam is composed of deuterons, an additional energy is delivered to the target with increased energy gain. Therefore ,in this innovative suggestion ,we consider deuterium beams for fast ignition in D+ 3 Hemixture and solve the dynamical balance equations under the available physical conditions by considering a new average reactivity formula ,then we compute the energy gain in this mixture .Our computational results show that we can get energy gain value larger than 4 at resonant temperature (200keV)of D+ 3 Hemixture. We select D+ 3 Hefuel, because D+3Hereaction is very attractive from a theoretical point of view since it does not produced neutrons. The D+3Hebenefits include full-lifetime materials, reduced radiation damage, less activation ,absence of tritium breeding blankets ,highly efficient direct energy conversion, easier maintenance, proliferation resistance.