Absorption properties of film-coupled log-periodic optical antennas in the near-infrared region are numerically investigated. The maximum absorption for TE and TM polarizations at normal incidence reach to 95% and 93%, respectively, and the optimal absorption of around 90% can be simultaneously obtained for both cases. It is shown that the main absorption peak is independent to light polarizations at normal incidence. Moreover, the log-periodic antenna-assisted absorption represents district polarization selectivity at high-order resonances. For oblique incidence, only the incident light of specific wavelengths within a narrow incidence angle can be almost entirely trapped inside the absorber, indicating special direction and wavelength selectivity of the absorber. All these features would lead to potential applications in photovoltaic technology, sensing, etc.