Offline map matching identifies corresponding roads to a GPS trajectory represented by a series of recorded geographic coordinates (GPS points) to the road network. This paper defines matching error as cost on the corresponding road-link to matched GPS points and formulates the offline map matching problem as a shortest path problem with resource constraints. By regarding matched points on one link as a type of resource consumed, the resource constraint indicates that the number of matched GPS points equals the total number of points in the given trajectory. We propose an offline map matching algorithm based on shortest paths by calculating the matching error on each link and extending the classic label-setting shortest path algorithm to find the path with the minimum total matching error for all GPS points. We use real-world taxi trajectories to compare our algorithm with three state-of-the-art map matching algorithms. Our algorithm outperforms all benchmark algorithms in terms of both matching accuracy and computational efficiency. Our algorithm achieves greater matched length (5.36 to 12.27% larger) and lower mis-matched length (3.72 to 75.30% smaller) at a very high matching speed (60.59 points per second on average over thirteen sampling intervals).