This article investigates exponential stability problems of switched nonlinear positive systems (SNPSs) with partial unstable subsystems and time-delay. Firstly, based on improved Halanay inequality technique combined with multiple max-separable Lyapunov functions, and designing mode dependent average dwell time (MDADT) switching strategies, sufficient conditions of exponential stability of the SNPS are obtained. Then, the conservatism of stability conditions is lower than the previous results due to no restrictions on minimum dwell time of each subsystem, and exponential stability conditions of switched positive linear systems including time-delay, as the special cases, are concluded. Finally, a given example is shown to illustrate the effectiveness of theoretical results.