Abstract: The differential branching fraction with respect to the dimuon invariant mass squared, and the CP asymmetry of the B-+/- -> pi(+/-)mu(+/-)mu(-) decay are measured for the first time. The CKM matrix elements vertical bar V-td vertical bar, and vertical bar V-ts vertical bar, and the ratio vertical bar V-td/V-ts vertical bar are determined. The analysis is performed using proton-proton collision data corresponding to an integrated luminosity of 3.0 fb(-1), collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. The total branching fraction and CP asymmetry of B-+/- -> pi(+/-)mu(+/-)mu(-) decays are measured to be B(B-+/- -> pi(+/-)mu(+/-)mu(-)) = (1.83 +/- 0.24 +/- 0.05) x 10(-8) and A(cp)(B-+/- -> pi(+/-)mu(+/-)mu(-)) = -0.11 +/- 0.12 +/- 0.01, where the first uncertainties are statistical and the second are systematic. These are the most precise measurements of these observables to date, and they are compatible with the predictions of the Standard Model.