Summary: ``In this paper, we consider the following abstract evolution equation with memory and time-varying delay of the form $$ u_{tt}(t)+Au(t)-\int^t_0g(t-s)Au(s){\rm d}s+\mu_1h_1(u_t(t))+\mu_2 h_2(u_t(x,t-\tau(t)))=\nabla F(u(t)). $$ By introducing suitable energy and Lyapunov functionals, and making use of some properties of the convex functions, we establish decay estimate for the energy, which depends on the behavior of $h_1$ and the relaxation $g$. The decay estimate can be applied to various concrete models. We shall also give some applications to illustrate our result.''