A kind of two-mode fiber with pure silica core and graded index is proposed by employing full vector finite element method,which combines the advantages of low differential mode group dela y (DMGD) of graded index few-mode fiber and low loss of pure silica core fiber.The proposed few-mode fiber obtains low loss,low DMGD,low bending loss and low mode crosstalk using the methods of pure silica core,graded index,the trench refr active index and large mode refractive index,respectively.Moreover, the nonlinear coefficient and DMGD of the proposed few mode fiber are flattened in the wavelength range of 1.5－1.65μm.