We investigate infrared colours and spectral energy distributions (SEDs) of 338 X-ray selected AGN from Swift-BAT 105-month survey catalogue that have AKARI detection, in order to find a new selection criteria for Compton-thick AGN. By combining data from Galaxy Evolution Explore (GALEX), Sloan Digital Sky Survey (SDSS) Data Release 14 (DR14), Two Micron All Sky Survey (2MASS), Wide-field Infrared Survey Explorer (WISE), AKARI and Herschel for the first time we perform ultraviolet (UV) to far-infrared (FIR) SED fitting 158 Swift BAT AGN by CIGALE and constrain the AGN model parameters of obscured and Compton-thick AGN. The comparison of average SEDs show while the mid-IR (MIR) SEDs are similar for the three AGN populations, optical/UV and FIR regions have differences. We measure the dust luminosity, the pure AGN luminosity and the total infrared (IR) luminosity. We examine the relationships between the measured infrared luminosities and the hard X-ray luminosity in the 14-195 keV band. We show that the average covering factor of Compton-thick AGN is higher compared to the obscured and unobscured AGN. We present a new infrared selection for Compton-thick AGN based on MIR and FIR colours ([9$mu$m - 22$mu$m]$ > 3.0$ and [22$mu$m - 90$mu$m]$ < 2.7$) from WISE and AKARI. We find two known Compton-thick AGN that are not included in the Swift-BAT sample, and conclude that MIR colours covering 9.7$mu$m silicate absorption and MIR continuum can be a promising new tool to identify Compton-thick AGN.
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