This paper is concerned with the problem of observer design for switched recurrent neural networks with time-varying delay. The attention is focused on designing the fullorder observers that guarantee the global exponential stability of the error dynamic system. Based on the average dwell time approach and the free-weighting matrix technique, delaydependent sufficient conditions are developed for the solvability of such problem and formulated as linear matrix inequalities. The error-state decay estimate is also given. Then, the stability analysis problem for the switched recurrent neural networks can be covered as a special case of our results. Finally, four illustrative examples are provided to demonstrate the effectiveness and the superiority of the proposed methods.