Abstract: In order to explore the nonlocal impact of memory terms on the blow-up solutions to high-order wave equations, the blow-up of solutions to the Moore-Gibson-Thompson equation with a nonlinear memory term is studied. With the time-dependent functional and the test function, the first lower bound and lower bound series of the functional are derived. Then, the nonexistence of solutions and the upper bound estimate of solutions for the lifespan are proved by applying iteration and slicing technique.