The initial value problem of the semi-linear plate equation with memory in multi-dimension **R*** ^{n}(n≥1)* is studied.In the Fourier space,we obtain the decay estimates of solutions to the linear problem.And through introducing a set of time-weighted Sobolev spaces and applying the contraction mapping theorem,we obtain the global in-time existence and the optimal decay estimates of solutions to the semi-linear problem under smallness assumption on the initial data.