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In this paper we consider the Cauchy problem for 2D viscous shallow watersystem in $H^s(\mathbb{R}^2)$, $s>1$. We first prove the local well-posednessof this problem by using the Littlewood-Paley theory, the Bony decomposition,and the theories of transport equations and transport diffusion equations.Then, we get the global existence of the system with small initial data in$H^s(\mathbb{R}^2)$, $s>1$. Our obtained result improves the recent result in\cite{W}

Global existence and well-posedness of 2D viscous shallow water system in Sobolev spaces with low regularity