To understand the connection between active galactic nuclei (AGNs) and star formation, we investigated the relation between AGN bolometric and far-infrared (FIR) luminosities, using type-2 AGNs. By matching type-2 AGNs at z < 0.3 selected from the SDSS based on the emission-line diagnostics, against the AKARI/FIS All-Sky Survey Catalogue and the COSMOS PEP (PACS Evolutionary Probe) Survey Catalogue, we obtained a sample of 729 type-2 AGNs detected in the AKARI survey ($90{mu}m$) and 17 ones detected in the PEP survey ($100{mu}m$). For AGN bolometric luminosities, we adopted an estimate based on the [OIII] and [OI] line luminosities. We confirmed that there is a correlation between the AGN bolometric and FIR luminosities with a large scatter, which is consistent with previous studies. However, we claim that this correlation suffers from various artificial effects, e.g., FIR detection limits, survey volumes, and so on. We will discuss the limitations of studying the connection between AGN and star formation using currently available facilities.