This paper is concerned with the surface and small scale effects on transverse vibration of a viscoelastic single-layered graphene sheet (SLGS) subjected to an in-plane magnetic field. The SLGS is surrounded by an elastic medium which is simulated as Visco-Pasternak foundation. In order to investigate the small scale effects, the nonlocal elasticity theory is employed due to its simplicity and accuracy. The effect of structural damping of SLGS is taken into account based on Kelvin’s model on elastic materials. An analytical method is used to obtain the natural frequency of the system. A detailed parametric study is conducted to elucidate the effects of the surface layers, nonlocal parameter, magnetic field, Visco-Pasternak elastic medium, viscoelastic structural damping coefficient and aspect ratio of graphene sheet. The findings indicate that enhancing the magnetic field and the density of surface layers leads to an increase in the natural frequency of SLGS.