Abstract: We consider the asymptotic behavior of solutions for non-autonomous FitzHugh-Nagumo system driven by additive white noise in Hilbert space.Firstly,we investigate the existence of random attractor of the random dynamical system generated by the solutions of considered system.Secondly,we present criterion for estimating an upper bound of the fractal dimension of a random invariant set of a random dynamical system on a separable Banach space.Finally,we apply expectation of some random variables and these conditions to prove the finiteness of fractal dimension of the random attractors for stochastic FitzHugh-Nagumo system driven by additive white noise.