In this paper, we study the dividend problems for finite time interval in the classical risk model. Assume that the dividends are paid according to a barrier strategy in the time interval $[0,t]$, i.e., given a nonnegative barrier value $b$, the dividends only can be paid when the surplus exceeds $b$ and the excess is paid as dividend. Applying the ``differential argument'', the equation for the total expected discounted dividends in the time interval $[0,t]$ ($V(x;t)$) is derived, and the
explicit expression for the Laplace transform of $V(x;t)$ with respect to $t$ is obtained under the assumption that the claim sizes are exponentially distributed. Finally, a numerical example is given by Stehfest method.