Abstract: In order to provide powerful criterion for resolving economy problem， after introducing the convergence theorem of reverse supermartingale, some stochastic stability and instability critenia of backward stochastic differential equation (BSDE) of Itô type is obtained by the method of Lyapunov function, including the pth moment exponential stochastic stability, almost sure exponential stochastic stability, the qth moment stochastic instability and so on.