Polyline curves which are composed of line segments and arcs are widely used in engineering applications. In this paper, a novel offset algorithm for polyline curves is proposed. The offset algorithm comprises three steps. Firstly, the offsets of all the segments of polyline curves are calculated. Then all the offsets are trimmed or joined to build polyline curves that are called untrimmed offset curves. Finally, a clipping algorithm is applied to the untrimmed offset curves to yield the final results. The offset algorithm can deal with polyline curves that are self-intersection, overlapping or containing small arcs. The new algorithm has been implemented in a commercial system TiOpenCAD 8.0 and its reliability is verified by a great number of examples.