In this paper, we are interested in a viscoelastic Moore-Gibson-Thompson equation with a type-II memory term and a relaxation function satisfying g'(t) <= -eta(t)g(t). By constructing appropriate Lyapunov functionals in the Fourier space, we establish a general decay estimate of the solution under the condition (beta -gamma/alpha - rho/2 ) > 0. We then give the decay rate of the L-2-norm of the solution. We also give two examples to illustrate our theoretical results.