In this paper the secure performance for the visible light communication (VLC) system with multiple eavesdroppers is studied. By considering the practical amplitude constraint instead of an average power constraint in the VLC system, the closed-form expressions for the upper and the lower bounds of the secrecy outage probability and the average secrecy capacity are derived. Since the locations for both legitimate receiver and eavesdroppers are unknown as well as random, the stochastic geometry method is introduced for problem formulation. Moreover, accurate expressions with a low computational complexity are obtained with the rigorous derivation. Simulation results verify the correctness of our theoretical analysis.