Glassy magnetic behavior has been observed in a wide range of crystalline magnetic materials called spin glass. Here, we report spin glass behavior in a structural glass of a magnetic ionic liquid, C4mimFeCl4. Magnetization measurements demonstrate that an antiferromagnetic ordering occurs at TN = 2.3 K in the crystalline state, while a spin glass transition occurs at TSG = 0.4 K in the structural glass state. In addition, localized magnetic excitations were found in the spin glass state by inelastic neutron scattering, in contrast to spin-wave excitations in the ordered phase of the crystalline sample. The localized excitation was scaled by the Bose population factor below TSG and gradually disappeared above TSG. This feature is highly reminiscent of boson peaks commonly observed in structural glasses. We suggest the "magnetic" boson peak to be one of the inherent dynamics of a spin glass state.