In this paper, We are consider a (2+1)-dimensional generalized Gardner equation with damping term is subjected to the Lie symmetry group method. Classification of its symmetry algebra into one- and two-dimensional subalgebras is carried out in order to facilitate its reduction systematically to (1+1)-dimensional partial differential equations and then to first order ordinary differential equations. Keywords: Nonlinear PDE, Lie’s Classical Method, Lie’s Algebra, and Symmetry group. AMS Code: 35G20, 78J70