Valley current, a stable, dissipationless current, originates due to the emergence of Berry curvature in inversion symmetry broken systems. Several theoretical predictions and experimental observations have explored layer symmetry breaking in AB-stacked bilayer graphene due to long-range Coulomb interactions between the electrons. However, none of the experimental studies conducted so far have observed valley current in unbiased bilayer graphene, which makes it vital to study the Berry curvature in unbiased bilayer graphene. In this study, we observed a non-zero Berry curvature with opposite values at K and K' valleys, validating the argumentation of the asymmetry persistent in unbiased bilayer graphene. The magnitude, as well as the polarity of the Berry curvature, is tunable with the application of an out-of-plane electric field. These results are especially important because they can lead to the realization of a valley valve, in which the carriers from the K and K' valleys can be regulated with a gate at the centre of a bilayer graphene nanoribbon.