The variational method is applied to the study of charge transfer in dry DNA by using an extended Holstein small polaron model in two cases: the site-dependent finite-chain discrete case and the site-independent continuous one. The treatments in the two cases are proven to be consistent in theory and calculation. Discrete and continuous treatments of Holstein model both can yield a nonlinear equation to describe the charge migration in an actual long-range DNA chain.Our theoretical results of binding energy Eb, probability amplitude of charge carrier φ and the relation between energy and charge-lattice coupling strength are in accordance with the available experimental results and recent theoretical calculations.