A multi-core optical amplifying fiber includes: core portions doped with a rare-earth element; an inner cladding portion; and an outer cladding portion. A mode field diameter of each core portion at a wavelength at which the rare-earth element performs optical amplification is 5 μm to 11 μm, a relative refractive-index difference of the maximum refractive index of each core portion with respect to the inner cladding portion is 0.35% to 2%, a core-to-core distance is set such that total inter-core crosstalk is −40 dB/100 m or lower in an optical amplification wavelength band subjected to the optical amplification, a cladding thickness is smaller than a value obtained by adding the mode field diameter to a minimum value of the core-to-core distance, and a ratio of a total sectional area of the core portions to a sectional area of the inner cladding portion is 1.9% or more.