The finger-vein pattern is one of the human biometric signatures that can be used for personal verification. The first task of a verification process using finger-vein patterns is extracting the pattern from an infrared finger image. As a robust extraction method, we propose the mean curvature method, which views the vein image as a geometric shape and finds the valley-like structures with negative mean curvatures. When the matched pixel ratio is used in matching vein patterns, experimental results show that, while maintaining low complexity, the proposed method achieves 0.25% equal error rate, which is significantly lower than what existing methods can achieve.