We consider the time-varying state-feedback stabilisation problem for a class of stochastic feedforward nonlinear systems with unknown growth rate in this paper. A new LaSalle-type theorem for stochastic time-varying systems is firstly established by using the generalized weakly positive definite function. As an application, to deal with serious uncertainties in the unknown growth rate, a time-varying approach, rather than an adaptive one, is adopted to design the scheme of a state-feedback controller for stochastic feedforward systems. Based on the established LaSalle-type theorem, it is shown that all signals of the resulting closed-loop system converge to zero almost surely. Illustrative examples are given to verify the theoretical findings.