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This paper is conced with the stability and robust stability of switched positive linear systems (SPLSs) whose subsystems are all unstable.By means of the mode-dependent dwell time approach and a class of discretized co-positive Lyapunov functions,some stability conditions of switched positive linear systems with all modes unstable are derived in both the continuous-time and the discrete-time cases,respectively.The copositive Lyapunov functions constructed in this paper are timevarying during the dwell time and time-invariant afterwards.In addition,the above approach is extended to the switched interval positive systems.A numerical example is proposed to illustrate our approach.