The authors show a Kirchhoff type plate equation with memory possesses a global attractor using a contraction function method. The precise equation under consideration is \[ u_{tt}+\alpha u_t+\Delta^2u-\int_0^\infty\mu(s)\Delta^2u(t-s)ds+\lambda u+(p-\beta\|\nabla u\|^2_2)\Delta u+f(u)=g(x), \] in \(\Omega\times\mathbb{R}^+\), where \(\Omega\subset\mathbb{R}^N,\) \(N\geq 1\), is a bounded domain with smooth boundary, \(\alpha\), \(\beta\), \(\lambda\) are positive constants, \(p\in\mathbb{R}\), \(\mu\) is a suitable memory kernel, and \(g\in L^2(\Omega)\) is a forcing term. Doubly-clamped boundary conditions are taken, and standard assumptions are taken on the nonlinear term (dissipation and critical growth conditions are given). Also, standard assumptions are used on the memory kernel (exponential fading). The existence of the global attractor follows Chapter 7 from the important book [I. Chueshov and I. Lasiecka, Von Karman evolution equations. Well-posedness and long-time dynamics. New York, NY: Springer (2010; Zbl 1298.35001)].