We explore the correlation between a boson peak and structural relaxation in a typical metallic glass. Consistent with enthalpy recovery, a boson peak shows a memory effect in an aging-and-scan procedure. Single-step isothermal aging produces a monotonic decrease of enthalpy and boson peak intensity; for double-step isothermal aging, both enthalpy and boson peak intensity experience, coincidently, an incipient increase to a maximum and a subsequent decrease toward the equilibrium state. Our results indicate a direct link between slow structural relaxation and fast boson peak dynamics, which presents a profound understanding of the two dynamic behaviors in glass.