We have measured continuous-wave (cw) photoinduced absorption (PA) spectra of PbS quantum dot (QD) films with four different sizes over a spectral range of 0.25-0.5 eV at T = 10 K. The PA spectrum shows a strong asymmetric IR absorption peak (IR-PA). Both the peak position and shape of this IR-PA indicate distinct confinement dependence. Combining with results of interband transitions and Stokes shift, we assign this IR-PA to a transition from a well-defined below-gap state to the second excitonic level (IP). By measuring the frequency dependence of this IR-PA, we estimate the lifetime of this below-gap state to be around several microseconds. Possible interpretations of the origin of this below-gap state are given. This transition could potentially be used to monitor photogenterated charge transfer in such QD systems.