Particle Imaging Velocimetry (PIV) estimates the flow of fluid by analyzing the motion of injected particles. The problem is challenging as the particles lie at different depths but have similar appearance and tracking a large number of particles is particularly difficult. In this paper, we present a PIV solution that uses densely sampled light field to reconstruct and track 3D particles. We exploit the refocusing capability and focal symmetry constraint of the light field for reliable particle depth estimation. We further propose a new motion-constrained optical flow estimation scheme by enforcing local motion rigidity and the Navier-Stoke constraint. Comprehensive experiments on synthetic and real experiments show that using a single light field camera, our technique can recover dense and accurate 3D fluid flows in small to medium volumes.