This paper mainly focuses on solitary waves excited by topography with time-dependent variable coefficient. By making use of multiple scale expansion and multiple level approximation method, a variable coefficient KdV equation with variable coefficient topographic forcing term is derived from barotropic and potential vorticity equation on a beta-plane including topography effect. In the derivation, removing y-average trick, a higher order term of stream function including five arbitrary functions and forced topography is introduced. Taking the strict solution of the standard constant coefficient KdV equation as the initial value, the approximate analytical solution of the derived equation is obtained by means of homotopy analysis method. Based on the new equation and its analytical solution, some complicated and changeable atmospheric blocking phenomena might be explained when some functions are selected appropriately.