In this paper, finite-time stability and boundedness for continuous positive switched systems with time-varying delay under state-dependent switching are investigated. By using a co-positive-type Lyapunov function method, sufficient conditions for solving the above-mentioned problems are given. It is proved that the sliding motion caused by the state-dependent switching will not destroy the performance of the system. The above results are extended to the discrete case. All the obtained results are formulated in the form of linear matrix inequalities (LMIs), which are computationally tractable. Finally, an illustrative example is given to verify the effectiveness of the proposed method.