Tensile elastic behavior of bulk Zr46(Cu4.5/5.5Ag1/5.5)46Al8 metallic glass was experimentally investigated. It exhibited linear and non-linear time-independent elastic deformation with a demarcative stress of approximately 500 MPa within the timescale in the present work, and repeated loading-unloading before yielding did not alter stress-strain relationship. The pure linear elastic strain limit is 0.6%, significantly lower than 2% as generally reported, but still much higher than 0.1% observed for typical crystalline alloys. Deviation from linear elastic behavior at stresses higher than 500 MPa is explained here as a macroscopic manifestation of local fluctuations in elastic strain, which becomes pronounced at stresses higher than the critical value. The occurrence of non-linear elasticity is possibly also related to the sinusoidal relationship between shear stress and atomic displacement.