We investigate the candidates of accelerator of ultra-high-energy cosmic rays (UHECRs) using the multi-wavelength spectral energy distributions, and discuss about the ability to accelerate UHECRs and constrain their physical conditions (acceleration site and size). The current experimental statistics of UHECRs is not sufficient for identification of the sources, although a spatial correlation between the arrival directions of UHECRs and nearby active galactic nuclei (AGNs) has been discussed using the data of the Pierre Auger Observatory and the Telescope Array. Some authors have discussed about the acceleration of UHECRs using various methods. Among them, Pe'er & Loeb (2012) derived constraints on the ability of AGNs to produce UHECRs by using observational quantities which are synchrotron peak luminosity and the peak flux ratio of inverse Compton scattering to synchrotron emission. For adopting this method, we need data of gammaray observation to determine the peak flux for high-energy region due to inverse Compton scattering. Thus, we focused on the Fermi Large Area Telescope gamma-ray sources. We investigated a spatial correlation between AGNs and the arrival directions of UHECRs, and we selected six AGNs as candidates of accelerator of UHECRs. We analyzed their spectral energy distributions by using multi-wavelength archival observational data. By introducing the constraints of Pe'er & Loeb (2012), we evaluate the physical conditions in the acceleration regions of these six AGNs and discuss whether they can accelerate to UHECRs. From the analysis, we found that three AGNs have ability to accelerate UHE protons to UHECRs in the AGN cores. Furthermore, we constrained the minimum size of the acceleration region for each source when UHE particles are accelerated in the AGN lobes. If UHE protons are accelerated, a few kpc-100 kpc are required as the minimum acceleration size. In the case of acceleration of heavy nucleus, the heavy particles can be accelerated in the AGN lobes if the size is larger than a few kpc. In this paper, we show that we achieved to establish a test method for individual candidate sources of acceleration of UHECRs.