The distribution of the received signals in many array processing applications are noncircular. Although optimal widely linear beamformer (WLB) can provide the best performance for noncircular received signals, its performance degrades severely under model mismatches in practical applications. As a remedy, we propose a robust WLB by using a precise reconstruction of extended interference-plus-noise covariance matrix (EINCM) and low-complexity estimator for the extended desired signal steering vector (EDSSV). We propose to first determine the steering vectors, powers and noncircularity coefficients of all signals and the noise power. In contrast to the previous reconstruction methods using the integration over a wide angular sector, we reconstruct the interference-plus-noise covariance matrix (INCM) and the pseudo INCM accurately according to their definitions. By using INCM and pseudo INCM, we can precisely reconstruct the EINCM. We propose to estimate the EDSSV by intersecting two extended subspaces respectively formed by eigendecomposing the extended sample covariance matrix and the extended desired signal covariance matrix. Unlike the convex optimization programming methods, this estimation of EDSSV does not require any optimization programs and yields to a solution with closed expression with low computational complexity. Simulation results demonstrate that the proposed robust WLB provides near optimal performance under several model mismatch cases.