The thermodynamic properties in one-dimensional S=1 Heisenberg antiferromagnet with single-ion anisotropy in the presence of a transverse magnetic field is obtained on the basis of the Schwinger boson mean-field theory. The anomalies of the specific heat at low temperatures, which might be an indicative of a field-induced transition from a Luttinger liquid phase to an ordered phase, are explicitly uncovered under the transverse field. A schematic phase diagram is proposed. The little effect of the single-ion anisotropy on specific heat is also observed, the result is very different from that obtained under a longitudinal field. All results above are expected to be helpful for the experimental investigation.