A study of two-pion scattering for the isospin channels, I = 0 and I = 2, using lattice QCD is presented. Mobius domain-wall fermions, on top of the Iwasaki-DSDR gauge action for gluons with periodic boundary conditions, are used for the lattice computations, which are carried out on two ensembles of gauge field configurations generated by the RBC and UKQCD Collaborations with physical masses, inverse lattice spacings of 1.023 and 1.378 GeV, and spatial extents of L = 4.63 and 4.58 fm, respectively. The all-to-all propagator method is employed to compute a matrix of correlation functions of two-pion operators. The generalized eigenvalue problem (GEVP) is solved for a matrix of correlation functions to extract phase shifts with multiple states-two pions with a nonzero relative momentum, as well as two pions at rest. Our results for phase shifts for both the I = 0 and I = 2 channels are consistent with the Roy equation and chiral perturbation theory, though at this preliminary stage our errors for I = 0 are large. An important outcome of this work is that we are successful in extracting two-pion excited states, which are useful for studying K -> pi pi decay, on physical-mass ensembles using the GEVP.