The quasi-one-dimensional S=1 antiferromagnet in magnetic field H is investigated with the exact diagonalization of finite chains and the mean-held approximation for the interchain interaction. In the presence of the single-ion anisotropy D, the full phase diagram in the HT plane is presented for H parallel to D and H perpendicular to D. The shape of the field-induced long-range ordered phase is revealed to be quite different between the two cases, as observed in the recent experiment of Ni(C5H14N2)(2)N-3(PF6) (NDMAP). The estimated ratio of the interchain and intrachain couplings of NDMAP (J'/J similar to 10(-3)) is consistent with the neutron-scattering measurement.