Abstract-Based on second-order cone programming, we present a new superdirective beamforming method with interferences and noise suppression for small aperture HF receive arrays. In the novel method, low side lobe level (SLL) and nulls are not only used to suppress interferences and noise, but also play an important part in overcoming the low array efficiency brought by superdirective beamforming. According to the actual condition, the new method can present a good tradeoff between directive gain, array efficiency, SLL, nulls and robustness against array uncertainty. Compared with the existing methods, it is more effective in suppressing interference and noise. The superiority and validity of the proposed method can be illustrated by numerical results.