Although many studies have been conducted to extract buildings from airborne lidar data, most of them assume that all the boundaries of a building are straight line segments. This makes it difficult to model building boundaries containing curved segments correctly. This paper aims to model buildings containing curved segments as combination of straight lines and arcs. First, two sets of boundary points are extracted by adaptive convex hull algorithm and local convex hull algorithm with a larger radius. Then, arc segments are determined by average spacing of boundary points and intersection ratio of perpendicular lines. Finally, building boundary is modeled through regularization of least squares line or circle fitting. The experimental results showed that the proposed method can model the curved building boundaries as arc segments correctly by completeness of 69% and correctness of 100%. The approach will be utilized effectively to create automatically digital map that meets the conditions of the Korean digital mapping.