A new concept of finite-time stability called stochastically finite-time attractiveness is defined for a class of stochastic nonlinear systems described by the Ito differential equation The settling time function is a stochastic variable and its expectation is finite A theorem and a corollary are given to verify the finite-time attractiveness of stochastic systems based on Lyapunov functions Two simulation examples are provided to illustrate the applications of the theorem and the corollary established in this paper (C) 2010 Elsevier Ltd All rights reserved