We present measurements of differential cross sections and decay asymmetries of incoherent φ-meson photo-production from the deuteron at forward angles using linearly polarized photons beam in energy range from the production threshold to E=2.4GeV. The experiment was performed at the SPring-8/LEPS facility. The differential cross section of incoherent production shows a large suppression compared with the free proton case. The reduction for the deuteron cannot be clearly explained in terms of simple isospin asymmetry. The decay asymmetry of incoherent φ photo-production shows that the eta exchange process is small. Since the exclusive K+K-p cross section shows the same reduction with incoherent, both the proton and neutron cross section reduce similarly. Consequently, the π-η interference effect is small too. The present results suggest that our understanding of φ photo-production within a nucleus should be rearranged.