We consider the initial boundary value problem for 2D g-Bénard equations in abounded domain with homogeneous Dirichlet boundary conditions. After studying the wellposedness of the problem, one is interested in asymptotic behavior of solutions when time is largeor tends to infinity, as it allows us to understand and eventually predict the development trends ofsuch systems in future, then we can make the appropriate adjustments to achieve the desiredresults. Specifically, for each given orbit of the system and an arbitrary time interval T, we canfind an orbit lying on the global attractor whose behavior when the time is large enough of thesetwo orbits is small enough in difference throughout the length T. In the paper, we study theexistence of the global attractor of the 2D g-Bénard equations. This is a compact invariant set,which contains much information about the asymptotic behavior of solutions. Our results extendsome outcomes by T.Q. Thinh and L.T. Thuy in Hnue journal of science (2020)