Vision-based localization and mapping in outdoor environments is still a challenging issue, which requests significant robustness against various unpredictable illumination changes. In this paper, an illumination-robust direct monocular SLAM system that focuses on modeling outdoor scenery is presented. To deal with global and local lighting changes, such as solar flares, the state-of-art illumination invariant photometric costs for RGB-D and stereo SLAM systems are revisited in the context of their monocular counterpart, where the camera motion and scene structure are jointly optimized with a reasonably poor initialization. Based on our analysis, a combined cost is proposed to achieve a high-precision motion estimation with an improved convergence radius. The proposed system is extensively evaluated on the synthetic and real-world datasets regarding accuracy, robustness, and processing time, where our approach outperforms systems with other costs and state-of-art DSO and ORBSLAM2 systems.