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We develop the Elastically Collective Nonlinear Langevin Equation theory to investigate, for the first time, glassy dynamics in capped metallic glass thin films. Finite-size effects on the spatial gradient of structural relaxation time and glass transition temperature (Tg) are calculated at different temperatures and vitrification criteria. Molecular dynamics is significantly slowed down near rough solid surfaces and the dynamics at location far from the interfaces is sped up. In thick films, the mobility gradient normalized by the bulk value well obeys the double-exponential form since interference effects between two surfaces are weak. Reducing the film thickness induces a strong dynamic coupling between two surfaces and flattens the relaxation gradient. The normalized gradient of the glass transition temperature is independent of vitrification timescale criterion and can be fitted by a superposition function as the films are not ultra-thin. The local fragility is found to remain unchanged with location. This finding suggests that one can use Angell plots of bulk relaxation time and the Tg spatial gradient to characterize glassy dynamics in metallic glass films. Our computational results agree well with experimental data and simulation.