Abstract We perform magnetohydrodynamic simulations to investigate the propagation of Alfvén waves in the magnetic chromosphere. We use the 1.5D expanding flux tube geometry setting and transverse perturbation at the bottom to generate the Alfvén wave. Compared with previous studies, our expansion is that we include the radiative loss term introduced by Carlsson & Leenaarts. We find that when an observation-based transverse wave generator is applied, the spatial distribution of the time-averaged radiative loss profile in our simulation is consistent with that in the classic atmospheric model. In addition, the energy flux in the corona is larger than the required value for coronal heating in the quiet region. Our study shows that the Alfvén wave-driven model has the potential to simultaneously explain chromospheric heating and how energy is transported to the corona.