We present performance studies of the Time-of-Flight (ToF) subdetector of the ATLAS Forward Proton (AFP) detector at the LHC. Efficiencies and resolutions are measured using high-statistics data samples collected at low and moderate pile-up in 2017, the first year when the detectors were installed on both sides of the interaction region. While low efficiencies are observed, of the order of a few percent, the resolutions of the two ToF detectors measured individually are 21 ps and 28 ps, yielding an expected resolution of the longitudinal position of the interaction, z _vtx, in the central ATLAS detector of 5.3 ± 0.6 mm. This is in agreement with the observed width of the distribution of the difference between z _vtx, measured independently by the central ATLAS tracker and by the ToF detector, of 6.0 ± 2.0 mm.