We solve numerically the Maxwell–Bloch equations using an iterative predictor-corrector finite-difference time-domain technique to study the propagation of femtosecond laser pulses in a strong two-photon absorption (TPA) organic molecular medium [ $4,4^{\prime }$ -bis(dimethylamino) stilbene]. The hybrid density functional theory is used to calculate electronic structures of the compound. The molecular system is described by a three-level model in an optical regime and has demonstrated a good optical power limiting behavior in a certain intensity region. Thresholds for the breakdown of optical power limiting are observed that are dependent on the input pulse width and, slightly, the propagation distance. The dynamical two-photon absorption cross section is obtained, which is almost a linearly increasing function of the pulse width in the femtosecond time domain. The propagation distance also has an obvious influence on the measurement of the TPA cross section, and nonmonotonic dependence of the TPA cross section on propagation distance is observed. The input pulse width and the thickness of the molecular samples thus should be taken into account when the TPA cross section is measured.