We have studied the star-forming and AGN activity of massive galaxies in the redshift range z = 0.4−2, which are detected in a deep survey field using the AKARI and Subaru telescopes toward the North Ecliptic Pole (NEP). The multi-wavelength survey allows us to select Mid-InfraRed (MIR) bright populations as Luminous InfraRed Galaxies (LIRGs) with L(IR) ≃ 1010–11 L⊙, which can be also sub-classified into Balmer Break Galaxies (BBGs) and Infra-Red (IR) Bump Galaxies (IRBGs). AKARI/IRC multiband photometry can distinguish their star-forming/AGN activity for LIRGs with/without the Polycyclic-Aromatic Hydrocarbon (PAH) emission bands at 6.2, 7.7 and 11.3 μm, and estimate the Star Formation Rate (SFR) from their total emitting InfraRed (IR) luminosities for star-formings and the emissions from dusty torus for AGNs. The results are summarised as below: 1) The rest-frame 7.7 μm luminosity is still a good tracer of the total IR (tIR) luminosity, as the PAH emission dominates for star-forming galaxies even up to z ≃ 2, 2) Rest-frame 5μm Luminosities may trace emissions from dusty torus of AGN in the LIRGs, 3) SFR of Starburst-AGN LIRGs (s/a-LIRGs) tends to quench at z < 0.8 more rapidly than that of Starburst dominated LIRGs (sb-LIRGs), 4) Intrinsic Stellar populations in the s/a-LIRGs show redder colours than those in the sb-LIRGs. These results suggest that Super Massive Black Holes (SMBH) could already have grown to ≃ 3 × 108M⊙ in the agn-LIRGs, with ≃ 1011L⊙ at z > 1.2, and the growth of SMBH tends to follow the star-forming activities around z = 1–2.