The authors discussed the existence of exponential attractors for abstract semigroups in Banach spaces. Let \(X\) be a Banach space, \(\{S(t)\;|\;t\geq 0\}\) be a semigroup on \(X\), \(\mathcal{A}\) be the global attractor of \(\{S(t)\;|\;t\geq 0\}\), and \(B_{\varepsilon_0}(\mathcal{A})\) denote the \(\varepsilon_0\)-neighborhood of \(\mathcal{A}\) in Banach space \(X\). The authors assume that there exists a positive constant \(T^*\) such that the operator \(S:=S(T^*)\) is of class \(C^1\) on a bounded absorbing set \(B_{\varepsilon_0}(\mathcal{A})\) and \(S: B_{\varepsilon_0}(\mathcal{A})\to B_{\varepsilon_0}(\mathcal{A})\), furthermore which linearized operator \(L\) at each point of \(B_{\varepsilon_0}(\mathcal{A})\) can be decomposed as \(L=K+C\) with \(K\) compact and \(\|C\|<\lambda<1\). Under such assumptions they firstly showed that the discrete semigroup \(\{S^n\,|\, n=0,1,2\cdots\}\) has an exponential attractor, then by the standard approach in [\textit{A. Eden} and \textit{C. Foias} et al, Exponential attractors for dissipative evolution equations. Research in Applied Mathematics 37. Chichester: Wiley, Paris: Masson (1994; Zbl 0842.58056)], they obtained the existence of an exponential attractor for the continuous semigroup \(\{S(t)\;|\;t\geq 0\}\). The abstract result is applied to some nonlinear reaction-diffusion equations with polynomial growth nonlinearity of arbitrary order.