The structural features in Manhattan world encode useful geometric information of parallelism, orthogonality and/or coplanarity in the scene. By fully exploiting these structural features, we propose a novel monocular SLAM system which provides accurate estimation of camera poses and 3D map. The foremost contribution of the proposed system is a structural feature-based optimization module which contains three novel optimization strategies. First, a rotation optimization strategy using the parallelism and orthogonality of 3D lines is presented. We propose a global binding method to compute an accurate estimation of the absolute rotation of the camera. Then we propose an approach for calculating the relative rotation to further refine the absolute rotation. Second, a translation optimization strategy leveraging coplanarity is proposed. Coplanar features are effectively identified, and we leverage them by a unified model handling both points and lines to calculate the relative translation, and then the optimal absolute translation. Third, a 3D line optimization strategy utilizing parallelism, orthogonality and coplanarity simultaneously is proposed to obtain an accurate 3D map consisting of structural line segments with low computational complexity. Experiments in man-made environments have demonstrated that the proposed system outperforms existing state-of-the-art monocular SLAM systems in terms of accuracy and robustness.