In many array processing, the received signals are nonstationary, or in particular, noncircular. Widely linear minimum variance distortionless response (WL MVDR) beamformers can exploit the noncircularity of received signals and improve the performance of the conventional MVDR beamformer. However, in the optimum WL MVDR beamformer, the array steering vector (ASV) and the signal noncircularity coefficient should be known a priori for the signal of interest. This requirement puts strict limitation to the implementation of this beamformer. We therefore in this paper propose a robust approach to the optimal WL MVDR beamformer that can deal with the uncertainties in the ASV and noncircularity coefficient. Two variants of the proposed approach are developed based on the treatment of the uncertainties. By doing so, the requirement on the exact information is relaxed while the performance improvement can still be obtained. Simulation studies are also provided to illustrate the performance of the proposed approach.