According to the pseudopotential plane-wave method of first-principles calculation based on the spin density functional theory, the electronic structure, magnetic and optical properties of laminated molybdenum oxides (orthonormal and monoclinic MoO₃) are studied theoretically. The interlaminar dissociation energy, band-structure, spin polarization, dielectric function, and the optical absorption/reflectivity in a charged state are systematically calculated to explore the potential technology applications of laminated MoO₃ as electrochromic or electromagnetic materials in optoelectronic devices. The semilocal GGA-PW91 and nonlocal HSE06 exchange-correlation functional are employed to obtain the more accurate crystal structure and band gap respectively. The cleavage energy results indicate that the single layers can easily flake off from the bulk material of these molybdenum oxides. The band structure and atomic-projected density of states prove that the conduction band minimum and valence band maximum are mainly derived from the atom-orbitals bonding oriented in layer-plane, representing characteristic two-dimensional electronic structure. The spin polarized calculations imply that the evident magnetic-moment will engender in MoO₆ octahedron layers of the perfect MoO₃ due to the substantial spin polarization of Mo and vertex O atoms which are ferromagnetic-coupling to produce significant net magnetic moments, essentially accounting for the magnetic source of bulk MoO₃. The Mo vacancy reduces the electronic density of states derived from the spin polarized d-orbitals, leading the net magnetic moment to decrease, while the O_I vacancy can reduce the density of spin-down states in the MoO₃, resulting in the significant improvement of net magnetic moment. The existence of O_II vacancy leads to the energetic spin-splitting of O-2p and Mo-4d orbital states, and thus increasing net magnetic moment by raising the electronic density of polarized spin-up states. The electron spin polarization of Mo-4d orbital component dominantly contributes to the bulk magnetism. The laminated MoO₃ presents a significant optical response in the visible region with obvious anisotropy of optical absorption spectra, which will represent a considerable blue shift or new low-frequency absorption peaks for visible light when loading charges. The calculation results demonstrate that the laminated molybdenum oxides have evident electrochromic property with controllable magnetic moment, which provides theoretical basis and technical data for developing novel functional materials with high performance to be used in electromagnetic or optoelectronic devices.