The subpath planning problem is a branch of the path planning problem, which has widespread applications in automated manufacturing process as well as vehicle and robot navigation. This problem is to find the shortest path or tour subject for travelling a set of given subpaths. The current approaches for dealing with the subpath planning problem are all based on meta-heuristic approaches. It is well-known that meta-heuristic based approaches have several deficiencies. To address them, we propose a novel approximation algorithm in the O(n^3) time complexity class, which guarantees to solve any subpath planning problem instance with the fixed ratio bound of 2. Also, the formal proofs of the claims, our empirical evaluation shows that our approximation method acts much better than a state-of-the-art method, both in result and execution time.