We report the first experimental results on the electromagnetic interference (EMI) shielding effectiveness (SE) of monolayer graphene. The monolayer CVD graphene has an average SE value of 2.27 dB, corresponding to similar to 40% shielding of incident waves. CVD graphene shows more than seven times (in terms of dB) greater SE than gold film. The dominant mechanism is absorption rather than reflection, and the portion of absorption decreases with an increase in the number of graphene layers. Our modeling work shows that plane-wave theory for metal shielding is also applicable to graphene. The model predicts that ideal monolayer graphene can shield as much as 97.8% of EMI. This suggests the feasibility of manufacturing an ultrathin, transparent, and flexible EMI shield by single or few-layer graphene.