A nonlinear random vibration model of a current carrying thin rectangular plate simply supported at each edge was established when the plate was applied mechanical load in a magnetic field. The model was proposed based on the theories of plates and shells and the magnetic elastic mechanics. It was simplified as a nonlinear dynamics differential equation by using Galerkin variation method. Then the equation was equivalent to be a one-dimensional It stochastic differential equation by applying the stochastic average theory of a quasi non-integrable Hamilton system. The local stochastic stability of the system was judged using the maximum Lyapunov index. Its global stability of the system was also judged using the singular boundary theory.Finally the influences of the system parameters on the stochastic Hopf bifurcation were researched through the steady probability density function. The numerical simulation results were shown in the paper.