A transient negative photovoltaic-response behavior was reported in a pixel of the linear array of HgCdTe infrared photovoltaic detectors. When irradiated with a picosecond pulsed laser， the time profile of the responding voltage shows an apparent negative valley during the first 15 ns， then it evolves a positive peak. By changing the excitation laser energy， the transient photo-responses of the detectors show the similar time evolution profiles， no matter for the case of single photon absorption transition that the photon energy is larger than the bandgap or for the case of two photon absorption transition that the photon energy is smaller than the bandgap. Blocking the laser beam with an aperture to limit the irradiation area makes the negative photovoltage decrease and even disappear. By considering the p-electrode configuration in the linear array of the detectors， the negative photovoltaic-response has been attributed to the Schottky contact behavior of the p-electrode. Such a new phenomenon could be used in characterizing the Ohmic contact of the p-electrode in this kind of photodetectors， and its sensitivity is expected to be much higher than that of the conventional I-V measurements.