This paper proposes a novel folding pattern for flexible extrinsic calibration of a camera and a 2D laser rangefinder (LRF). The proposed pattern consists of multiple foldable facets. By folding and unfolding the facets, we can easily adjust the sizes and expanding angles of the pattern so that it can be observed by sensors with different view angles at different distances. Moreover, the folding pattern can have different numbers of facets such that it can flexibly generate different constraints to simplify the calibration process. The proposed pattern is thus very flexible and practical. Another important feature is that the proposed method does not require computing the metric information of the pattern, such as plane normal and distance, as required in existing methods. Therefore, it can further simplify the calibration process and enhance the calibration accuracy. In this method, we first derived a linear solution, and then refined the solution with the particle swarm optimization (PSO) method by both enforcing the rotation constraint and minimizing the sum of the square of the point-to-line distances. The proposed calibration pattern and method have been validated with both simulation and real data. Experimental results show that the method is very flexible and accurate for the extrinsic calibration of a camera and a 2D LRF.