The existence and uniqueness of the global solution of Cauchy problem for a class of non-linear heat conduction equation are discussed in this paper.By utilizing the estimation of energy and the estimation of degeneration together

and by the Banach fixed point theorem

the existence and uniqueness of the global solution are presented

as the initial value φ and the non-linear term a(x)u~β｜u｜~γ satisfy some certain conditions.