We consider a stochastic interacting vortex system of N particles, approximating the vorticity formulation of 2-D Navier-Stokes equation on torus. The singular interaction kernel is given by the Biot-Savart law. We only require the initial state to have finite energy, and obtain a sample-path large deviation principle for the empirical measure when the number of vortices goes to infinity. We utilizes a energy dissipation structure  to control the singular term and the rate function is characterized by an explicit formula supporting on sample paths with finite energy and finite integral of L2 norms over time.

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