The conventional minimum variance distortionless response (MVDR) beamformer becomes suboptimal when the signals are noncircular, and performance of the optimal widely linear MVDR beamformer may degrade for finite number of training samples. To circumvent this issue, the minimum sensitivity based widely linear MVDR beamformer is proposed, which utilizes the noncircularity of the signals of interest and the interference signals. The optimal weight vector is derived by using the minimum sensitivity criterion. Simulation results demonstrate that the proposed method has a better performance in the case of low signaltonoise ratio and snapshot deficiency.