Summary: We consider the existence and asymptotic behavior of the global weak solutions to a two-dimensional (2D) viscous liquid-gas two-phase flow model. The analysis is based on several key a priori estimates, which are obtained by the ideas of studying the single-phase Navier-Stokes equations. This can be viewed to be a generalization of the results in [S. Evje and K. H. Karlsen, J. Differ. Equations 245, No. 9, 2660–2703 (2008; Zbl 1148.76056)] from one dimension to two dimensions.