In this paper, the finite-time stability for a class of switched nonlinear positive systems of degree one is investigated under the mode-dependent average dwell time(MDADT) switching signal. Firstly, by constructing an appropriate switched max-type separate Lyapunov function, based on the MDADT switching signal, a sufficient condition for the finite-time stability of the switched nonlinear positive systems is given with the aid of Dini derivative. Comparision with the existing results of exponential stability, it further illustrates the difference between finite-time stability and exponential stability. Secondly, the result is applied to the switched linear positive systems, and some sufficient conditions for the finite-time stability of the switched linear positive systems under MDADT or average dwell time(ADT) switching signals are obtained. Finally, the simulation examples are given to illustrate the effectiveness of the conclusion.