We use the infinite volume reconstruction method to calculate the charged and neutral pion mass difference. The hadronic tensor is calculated using lattice QCD and then combined with an analytic photon propagator, and the mass splitting is calculated with exponentially suppressed finite-volume errors. The calculation is performed using six gauge ensembles generated with 2+1-flavor domain wall fermions, and five ensembles are at the physical pion mass. Both Feynman and Coulomb gauges are adopted in the calculation and agree well when the lattice spacing approaches zero. After performing the continuum extrapolation and examining the residual finite-volume effects, we obtain the pion mass splitting Δm_{π}=4.534(42)_{stat}(43)_{sys} MeV, which agrees well with experimental measurements.