In this paper, the exponential stability of continuous time positive impulse switched linear systems (PISLSs) with time-varying delays and unstable subsystems is studied. Firstly, by controlling the impulse within a reasonable range, a new linear copositive Lyapunov-Krasovskii functional is constructed, and the sufficient conditions for the stability of the considered system are given. Secondly, compared with the existing research results, when there exists impulse phenomenon, the state divergence generated by unstable subsystems can also be effectively compensated by dwell time switching, so that the improved stability criterion can be applied to the unstable situation of all subsystems. Finally, a simple example is given to verify the validity of the theoretical results.