Summary: By adapting a method of A. Kiselev, F. Nazarov and A. Volberg [Invent. Math. 167, No. 3, 445–453 (2007; Zbl 1121.35115)] with a suitable modification, we show that the critical dissipative quasi-geostrophic equations in \(\mathbb R^2\) has global well-posedness with arbitrary \(H^1\) initial data. A decay in time estimate for homogeneous Sobolev norms of solutions is also discussed.