We report the coherent excitation of the vibrational state of hydrogen molecules by two-photon absorption and the resultant third-harmonic generation (THG). Parahydrogen molecules cooled by liquid nitrogen are irradiated by mid-infrared nanosecond pulses at 4.8 mu m with a nearly Fourier-transform-limited linewidth. The first excited vibrational state of parahydrogen is populated by two-photon absorption of the mid-infrared photons. Because of the narrow linewidth of the mid-infrared pulses, coherence between the ground and excited states is sufficient to induce higher-order processes. Near-infrared photons from the THG are observed at 1.6 mu m. The dependence of the intensity of the near-infrared radiation on mid-infrared pulse energy, target pressure, and cell length is determined. We used a simple formula for THG with consideration of realistic experimental conditions to explain the observed results.