The possibility of measuring the proton electromagnetic form factors in the time-like region at FAIR with the ANDA detector is discussed. Detailed simulations on signal efficiency for the annihilation of + p into a lepton pair as well as for the most important background channels have been performed. It is shown that precise measurements of the differential cross-section of the reaction + p e - + e + can be obtained in a wide kinematical range. The determination of the ratio R of the moduli of the electric and magnetic proton form factors will be possible up to a value of momentum transfer squared of q 2 ≃ 14 (GeV/ c )^2 with absolute precision from 0.01 to 0.5 (for R ∼ 1 . The total + p e - + e + cross-section will be measured up to q 2 ≃ 28 (GeV/ c )^2. The results obtained from simulated events are compared to the existing data. Sensitivity to the two-photon exchange mechanism is also investigated.