The invention relates to a single mode fiber with a low damping coefficient. The single mode fiber with the low damping coefficient comprises a core layer and a cladding layer and is characterized in that the radius r1 of the core layer is 3.9-4.6Mum, the relative index of refraction delta1of the core layer is 0.08%-0.24%, the core layer covers an inner cladding layer, an concaving inner cladding layer, an auxiliary outer cladding layer and an outer cladding layer from interior to exterior, wherein the radius r2 of the inner cladding layer is 8-15Mum, the relative index of refraction delta2 of the inner cladding layer is-0.30 %--0.05 %,the radius r3 of the concaving inner cladding layer is 14-20Mum, the relative index of refraction delta3 of the concaving inner cladding layer is -0.6 %--0.2 %, the radius r4 of the auxiliary outer cladding layer is 35-50Mum, and the relative index of refraction delta4 of the auxiliary outer cladding layer ranges from -0.35 % to -0.05 %. The outer cladding layer is a pure silicon dioxide glass layer. The single mode fiber with the low damping coefficient has the advantages that the damping coefficient of a fiber is reduced, and through the reasonable design on the section face of each core and cladding layer of the fiber, the fiber is provided with a MFD equal to or larger than 8.7Mum; the section face of the fiber adopts a multilayer step-pattern concaving cladding structure, the wide cladding structure is used for limiting fundamental mode reveal, and a good improvement function on the bending loss of the fiber is achieved.