For a sensorless predictive current controlled boost dc-dc converter, its small-signal model that contains a number of parasitic parameters, is derived in this paper. This model indicates that the type of system becomes type 0 even with the correction of voltage loop proportional-integral controller, leading to the existence of output voltage steady-state error. Then a self-correction differential current observer (SDCO) is proposed to eliminate this steady-state error and gain high transient response speed. The self-correction part of the SDCO makes the system become type 1 to achieve no steady-state error for output voltage, whereas the differential part can guarantee that the intermediate calculation results do not overflow. By carrying out a series of simulation verifications, further investigation proves that the proposed algorithm has good robustness. Finally, the effectiveness of the proposed algorithm is verified by experimental results.