A graph is called -VPG, for some constant , if it has a string representation on an axis-parallel grid such that each vertex is a path with at most bends and two vertices are adjacent in if and only if the corresponding paths intersect each other. The part of a path that is between two consecutive bends is called a segment of the path. In this paper, we study the Maximum-Weighted Independent Set problem on -VPG graphs. The problem is known to be NP-complete on -VPG graphs, even when the two segments of every path have unit length [12], and -approximation algorithms are known on -VPG graphs, for [3, 14]. In this paper, we give a -approximation algorithm for the problem on -VPG graphs for any , where is the length of the longest segment among all segments of paths in the graph. Notice that is not required to be a constant; for instance, when , we get an -approximation or we get an -approximation when is a constant. To our knowledge, this is the first -approximation algorithm for a non-trivial subclass of -VPG graphs.