Abstract This paper investigates the problem of stabilization for a class of switched nonlinear systems with time-delay. Based on the differential mean value theorem (DMVT), the switched nonlinear systems are transformed into switched linear parameter varying (LPV) systems. By using multiple Lyapunov function approach and convexity principle, and via observer-based output feedback, a sufficient condition for the stabilization of the original system is proposed, which has been expressed in terms of linear matrix inequalities (LMIs). Further, the control method is extended to a class of switched nonlinear systems with norm-bounded uncertainties. A new sufficient condition is proposed, which guarantees the class of uncertain switched systems, is asymptotically stabilizable. Finally, two examples are given to illustrate the effectiveness of the proposed approaches.