Abstract: It usually takes a long observing time when a cognitive radar transmits the High-Range-Resolution (HRR) stepped-frequency signal. To save time, partial pulses of the stepped-frequency signal are transmitted to obtain the incomplete frequency data, and a Bayesian reconstruction algorithm is proposed to reconstruct the corresponding full-band frequency data. Firstly, the Complex Beta Process Factor Analysis (CBPFA) model is utilized to statistically model a set of full-band frequency data, whose probability density function (pdf) can be learned from this CBPFA model. Secondly, when the target is tracked and its attitude changes not much, the cognitive radar can just transmit the partial pulses of the stepped-frequency signal, and the corresponding full-band frequency data can be analytically reconstructed from the incomplete frequency data via the Compressive Sensing (CS) method and Bayesian criterion based on the previous pdf learned with CBPFA model. The reconstruction experiments of the measured HRR data demonstrate the performance of the proposed method.