© 2014 The Authors. A model-dependent amplitude analysis of B±→DK± with D→KS0π+π- decays is performed using proton-proton collision data, corresponding to an integrated luminosity of 1fb-1, recorded by LHCb at a centre-of-mass energy of 7 TeV in 2011. Values of the CP violation observables x± and y±, which are sensitive to the CKM angle γ, are measured to bex-=+0.027±0.044-0.008+0.010±0.001,y-=+0.013±0.048-0.007+0.009±0.003,x+=-0.084±0.045±0.009±0.005,y+=-0.032±0.048-0.009+0.010±0.008, where the first uncertainty is statistical, the second systematic and the third arises from the uncertainty of the D→KS0π+π- amplitude model. The value of γ is determined to be (84-42+49)°, including all sources of uncertainty. Neutral D meson mixing is found to have negligible effect.