The optimal widely linear (WL) minimum variance distortionless response (MVDR) beamformer, which has a powerful performance for the reception of a noncircular signal, was proposed by Chevalier et al. in 2009. Nevertheless, in spectrum monitoring or passive listening, the optimal WL MVDR beamformer is hard to implement due to an unknown second-order (SO) noncircularity coefficient. This paper aims at estimating the time-averaged SO noncircularity coefficient of a desired noncircular signal, whose waveform is unknown but whose steering vector is known, in the context of the optimal WL MVDR beamformer. The proposed noncircularity coefficient estimator can process 2N − 1 rectilinear signals at most using an array of N sensors. Moreover, a frequency-shift WL MVDR beamforming algorithm is proposed for a noncircular signal having a nonnull frequency offset or carrier residue, jointly with the estimation of the frequency offset of the rectilinear signal. Due to the inevitable estimation error of the time-averaged SO noncircularity coefficient, a diagonal loading technique is used to enhance the robustness of the optimal WL beamformers. Simulations are shown to verify the effectiveness of the proposed algorithms.