A multi-core optical fiber comprising: a plurality of core portions (10, 20, 30, 40, 50, 60, 70); and a cladding portion positioned at outer peripheries of the plurality of core portions, the cladding portion having a refractive index lower than a maximum refractive index of each of the core portions, wherein each of the core portions consists of a center core portion (11, 21, 31, 41, 51, 61, 71) having the maximum refractive index, and an outer periphery core portion (12, 22, 32, 42, 52, 62, 72) formed at an outer periphery of the center core portion and having refractive index which is lower than the refractive index of the cladding portion, a relative refractive index difference Δ1 of the center core portion relative to the cladding portion is 0.2% to 0.5%, a relative refractive index difference Δ2 of the outer periphery core portion relative to the cladding portion is equal to or greater than -0.5% and lower than 0%, a diameter of the center core portion is 14 μm to 19 μm, and a ratio of an outer diameter of the outer periphery core portion relative to the diameter of the center core portion is greater than 1 and equal to or lower than 4, a separation distance between each of the core portions and adjacent one of the core portions is equal to or shorter than 100 μm, each of the core portions propagates light only with predetermined number, which is equal to or greater than 2, of propagation modes, an effective core area at wavelength of 1550 nm of each of the propagation modes is equal to or greater than 120 μm 2,and a cross-talk of light at wavelength of 1550 nm between the respective propagation modes between the respective core portions is equal to or lower than -30.0 dB per 100 km of a propagation distance. a plurality of core portions (10, 20, 30, 40, 50, 60, 70); and a cladding portion positioned at outer peripheries of the plurality of core portions, the cladding portion having a refractive index lower than a maximum refractive index of each of the core portions, wherein each of the core portions consists of a center core portion (11, 21, 31, 41, 51, 61, 71) having the maximum refractive index, and an outer periphery core portion (12, 22, 32, 42, 52, 62, 72) formed at an outer periphery of the center core portion and having refractive index which is lower than the refractive index of the cladding portion, a relative refractive index difference Δ1 of the center core portion relative to the cladding portion is 0.2% to 0.5%, a relative refractive index difference Δ2 of the outer periphery core portion relative to the cladding portion is equal to or greater than -0.5% and lower than 0%, a diameter of the center core portion is 14 μm to 19 μm, and a ratio of an outer diameter of the outer periphery core portion relative to the diameter of the center core portion is greater than 1 and equal to or lower than 4, a separation distance between each of the core portions and adjacent one of the core portions is equal to or shorter than 100 μm, each of the core portions propagates light only with predetermined number, which is equal to or greater than 2, of propagation modes, an effective core area at wavelength of 1550 nm of each of the propagation modes is equal to or greater than 120 μm 2,and a cross-talk of light at wavelength of 1550 nm between the respective propagation modes between the respective core portions is equal to or lower than -30.0 dB per 100 km of a propagation distance.