Abstract: Using 9fb^-1 data collected with the BESIII spectrometer at the Beijing Electron Positron Collider II storage ring, the production cross section of the e⁺e^－→π^＋π^－J/ψ process was measured. We observed the Y(4260) resonance and measured its parameters with the best precision to date in the world. Our measurement shows that the mass of Y(4260) is around 4.22 GeV/c² and its width is about 44 MeV, which are lower and much narrower, respectively, than previous measurements. BESIII's precise measurement sets a tighter constraint on the interpretation of the Y(4260) internal structure models compared with previous experiments. In ddition, BESIII also observed a new resonance near 4.32 GeV/c², with a statistical significance of 7.6σ. The mass and width of this resonance agree with the Y(4360) state within experimental error.