In this paper, the following initial boundary value problem of the nonclassical diffusion equation \[ u_t-\nu\Delta u_t- \lambda\Delta u+ g(u)= f(x),\quad (x,t)\in \Omega\times \mathbb{R}^+,\tag{1} \] \[ u(x,0)= u_0(x),\quad x\in\Omega, \] \[ u(x,t)= 0,\quad (x,t)\in \partial\Omega\times \mathbb{R}^+ \] is considered, where \(\lambda\) is a positive constant, \(g: \mathbb{R}\to\mathbb{R}\) is a smooth function, \(f\in L^2(\Omega)\) and \(\Omega\subset\mathbb{R}^n\) is a smooth bounded open set. The aim of this paper is to show the existence of a finite-dimensional exponential attractor for this equation. First, the Lipschitz continuity of the dynamical system \(S(t)\) associated with the equation (1) is established. Then the squeezing property for the semigroup \(S(t)\) is shown and the existence of the finite fractal dimensional exponential attractor is deduced.