Non-Hermitian skin effect and photonic topological edge states are of great interest in non-Hermitian physics and optics. However, the interplay between them is largely unexplored. Here, we propose and demonstrate experimentally the non-Hermitian skin effect constructed from the nonreciprocal flow of Floquet topological edge states, which can be dubbed "Floquet skin-topological effect." We first show the non-Hermitian skin effect can be induced by structured loss when the one-dimensional (1D) system is periodically driven. Next, based on a two-dimensional (2D) Floquet topological photonic lattice with structured loss, we investigate the interaction between the non-Hermiticity and the topological edge states. We observe that all the one-way edge states are imposed onto specific corners, featuring both the non-Hermitian skin effect and topological edge states. Furthermore, a topological switch for the skin-topological effect is presented by utilizing the phase-transition mechanism. Our experiment paves the way for realizing non-Hermitian topological effects in nonlinear and quantum regimes.