Manhattan and Atlanta worlds hold for the structured scenes with only vertical and horizontal dominant directions (DDs). To describe the scenes with additional sloping DDs, a mixture of independent Manhattan worlds seems plausible, but may lead to unaligned and unrelated DDs. By contrast, we propose a novel structural model called Hong Kong world. It is more general than Manhattan and Atlanta worlds since it can represent the environments with slopes, e.g., a city with hilly terrain, a house with sloping roof, and a loft apartment with staircase. Moreover, it is more compact and accurate than a mixture of independent Manhattan worlds by enforcing the orthogonality constraints between not only vertical and horizontal DDs, but also horizontal and sloping DDs. We further leverage the structural regularity of Hong Kong world for the line-based SLAM. Our SLAM method is reliable thanks to three technical novelties. First, we estimate DDs/vanishing points in Hong Kong world in a semi-searching way. We use a new consensus voting strategy for search, instead of traditional branch and bound. This method is the first one that can simultaneously determine the number of DDs, and achieve quasi-global optimality in terms of the number of inliers. Second, we compute the camera pose by exploiting the spatial relations between DDs in Hong Kong world. This method generates concise polynomials, and thus is more accurate and efficient than existing approaches designed for unstructured scenes. Third, we refine the estimated DDs in Hong Kong world by a novel filter-based method. Then we use these refined DDs to optimize the camera poses and 3D lines, leading to higher accuracy and robustness than existing optimization algorithms. In addition, we establish the first dataset of sequential images in Hong Kong world. Experiments showed that our approach outperforms state-of-the-art methods in terms of accuracy and/or efficiency.