This paper introduces a novel finger motion capture system using FBG (fiber Bragg grating) optical sensors. We develop two types of sensors to seamlessly reconstruct finger motion from strains induced in the FBGs. First, the shape sensor incorporates three optical fibers with multiple FBGs to reconstruct the position and orientation of a finger joint in 3D. In addition, the angle sensor is designed to measure the high curvature of bending on the finger joints. By deploying the two types of sensors on the fingers, we can reconstruct various finger motion in real time without drift over time. The accuracies of the fabricated FBG sensors are evaluated, resulting in an average error of 1.49 mm for the shape sensor at the distal tip (1.9% for the full length of the sensor) and 0.21° error for the angle sensor. We finally demonstrate finger motion tracking with the FBG sensors in real time, while measuring the multi-DOF motion at the carpometacarpal joint of the thumb and also the high curvatures of bending motion at the metacarpophalangeal and interphalangeal joints of the thumb and the index finger.