Radar high-resolution range profile (HRRP) has received intensive attention from the radar automatic target recognition (RATR) community. Usually, since the initial phase of a complex HRRP is strongly sensitive to target position variation, only the amplitude information in complex HRRPs is used for RATR, whereas the phase information is discarded. However, the remaining phase information except for initial phases in complex HRRPs may also contain valuable target discriminant information. RATR using complex HRRPs is discussed. The complex HRRPs' feature subspace within each target-aspect sector is extracted via principal component analysis as the corresponding template during the training phase; while in the test phase we decide that a test sample belongs to the feature subspace which has the test sample's minimum reconstruction error approximation. It is shown that the whole process is independent of the initial phases, but exploits the remaining phase information in complex HRRPs. Furthermore, to make the proposed recognition method more practical, a fast time-shift compensation algorithm is proposed. In the recognition experiments based on measured data, the proposed recognition method using complex HRRPs achieves better recognition results than that using only the amplitude vectors of the complex HRRPs.