The diffuse γ-ray emission from local molecular clouds is a powerful probe of local cosmic rays and interstellar gas. Here we report a γ-ray analysis for the Chamaeleon molecular-cloud complex using Fermi Large Area Telescope (LAT) data. The Chamaeleon molecular cloud is located in the solar neighborhood at a distance of about 150 pc. In previous Fermi-LAT analyses of the Chamaeleon region (Ackermann et al. 2012 and Planck Collaboration XXVIII, 2015), the γ-ray emitting interstellar gas was mainly decomposed into three components: atomic hydrogen, molecular hydrogen and some excess gas not traced properly by standard HI and CO surveys. In this analysis, we take a different approach and examine total column density (NH) models based on the dust optical depth at 353 GHz (τ353) obtained with Planck observations. Recent studies of the relation between NH and dust optical depth in local molecular clouds found a large deviation from a simple linear relation (e.g., Roy et al. 2013 and Planck Collaboration XXVIII, 2015), possibly due to evolutions of dust grains in cores of clouds. In fitting γ-ray data with several NH models, including both linear and non-linear relations with τ353, we found that a non-linear relation of τ353 proportional to the ∼1.3-th power of NH gives the best fit, which may indicate dust evolutions in high density regions.