This article considers the master-slave Markovian jump complex dynamical networks (CDNs) with multiple time-varying delays by designing a non-fragile sliding mode control mechanism to achieve H 1 /passive synchronization. First, by introducing a non-fragile sliding surface, master-slave CDNs can achieve H 1 /passive synchronization, and the state trajectory of CDNs can arrive the sliding surface based on a suitable controller. By applying an appropriate Lyapunov-Krasovskii functional (LKF) that combines triple and four integral terms, using the reciprocal convex combination method and utilizing a few novel integral inequalities, the criterion of H 1 /passive synchronization is established for master-slave CDNs. Besides, the prospective criterion of H 1 /passive synchronization can be transformed into the form of linear matrix inequalities. Moreover, reasonability of theoretical results is proved via numerical simulations.