A small core-diameter graded-index optical fiber include a core layer and a cladding having an inner cladding layer, a depressed cladding layer, and an outer cladding layer from inside to outside thereof. The core layer has a parabolic refractive index profile with a distribution index in a range of 1.9-2.1, a radius in a range of 10-21 μm, and a Δ1 max in a range of 0.7-1.7% at a core layer center, and is a silica glass layer co-doped with germanium, phosphorus, and fluoride. The inner cladding layer is a pure silica layer or an F-doped silica glass layer, and has a unilateral width in a range of 0.5-5 μm and a Δ2 in a range of −0.4-0%. The depressed cladding layer has a unilateral width in a range of 2-10 μm and a Δ3 in a range from −0.8% to −0.2%. The outer cladding layer is a pure silica glass layer.