In this paper, we derive the period-luminosity (P-L) relation for Large Magellanic Cloud (LMC) Cepheids based on mid-infrared AKARI observations. AKARI's Infrared Camera sources were matched to the Optical Gravitational Lensing Experiment-III (OGLE-III) LMC Cepheid catalogue. Together with the available I-band light curves from the OGLE-III catalogue, potential false matches were removed from the sample. This procedure excluded most of the sources in the S7 and S11 bands; hence, only the P-L relation in the N3 band is derived in this paper. Random-phase corrections were included in deriving the P-L relation for the single-epoch AKARI data; even though the derived P-L relation is consistent with the P-L relation without random-phase correction, however there is an similar to 7 per cent improvement in the dispersion of the P-L relation. The final adopted N3-band P-L relation is N3 = -3.246 log(P) + 15.844, with a dispersion of 0.149.