An attempt has been made to calculate the ground-state and first-excited-state energies of two-dimensional large magnetopolarons by using recently introduced squeezed Landau states. These states are obtained through the application of the two-mode coupled squeezed operator to the coherent states, and then a variational method is used to eliminate squeezing parameters. In the framework of this approach we obtain the ground- and first-excited-state energies of two-dimensional magnetopolarons.