Polygonal approximation is an effective yet challenging digital curve representation for image analysis, pattern recognition and computer vision. This paper proposes a novel approach, integer particle swarm optimization (iPSO), for polygonal approximation. When compared to the traditional binary version of particle swarm optimization (bPSO), the new iPSO directly uses an integer vector to represent the candidate solution and provides a more efficient and convenient means for solution processing. The velocity and position updating mechanisms in iPSO not only have clear physical meaning, but also guarantee the optimality of the solutions. The method is suitable for polygonal approximation which could otherwise be an intractable optimization problem. The proposed method has been tested on commonly used synthesized shapes and lake contours extracted from the maps of four famous lakes in the world. The experimental results show that the proposed iPSO has better solution quality and computational efficiency than the bPSO-based methods and better solution quality than the other state-of-the-art methods.