We report on a lattice QCD calculation of the flavor-singlet axial coupling constant g(A) of the proton from the axial-vector current. The simulation is carried out at beta = 6 on a quenched 16(3) X 24 lattice. An extrapolation to the chiral limit shows that the connected insertion (valence and cloud parts) is 0.62 +/- 0.09, which is close to g(A)(8). The disconnected insertion (vacuum polarization from the sea quark) for the u or d quark is -0.12 +/- 0.01 and the s quark also contributes -0.12 +/- 0.01. The total g(A)(0) is thus 0.25 +/- 0.12, which is in agreement with experiments. In addition, we find g(A)(3) = 1.20 +/- 0.11, g(A)(8) = 0.61 +/- 0.13, and F-A/D-A = 0.60 +/- 0.02, also in agreement with experiments.