We have studied detailed carrier generation process in the two-step photon absorption and influence of thermal carrier escape in quantum-dot intermediate-band solar cells (QD-IBSC). The photocurrent created by the two-step photon absorption shows saturation as the inter-band excitation intensity becomes strong, and the inter-band excitation intensity showing the saturation behavior strongly depends on the inter-subband excitation intensity. To interpret this phenomenon, we carried out a theoretical simulation based on carrier dynamics considering carrier generation, energy relaxation and thermal carrier escape. The results indicate that the photocurrent saturation is caused by filling the intermediate states. The shift of the saturation point depending on the inter-subband excitation intensity is caused by the shift of the quasi-Fermi level for the intermediate states.