The partial adaptive concentric ring array (CRA) has been successfully applied to 3-D beamforming because of its flexibility, faster tracking ability and reduced computation with respect to the fully adaptive CRA. In some cases, prior knowledge regarding some interferences is available so that better beamformers can be designed. The previous method that exploits prior knowledge by using a fixed penalty factor could not guarantee in maintaining a low residual interference and noise level. We propose in this paper an adaptive beamformer that automatically seeks out the optimum penalty factor to achieve the best performance. The proposed beamformer outperforms the previous design in maintaining a higher output signal to interference and noise ratio, even after the characteristics of the interferences have changed. The performance of the proposed beamformer is evaluated through simulations.