This paper is concentrated on the secure synchronization control issue for complex dynamical networks (CDNs) subjected to multiple attacks. For the sake of conserving resources and being closer to reality, a new output feedback controller based on pinning nodes is firstly designed. Secondly, in contrast with the existent researches on secure network circumstances, we establish a novel multiple attacks model considering the influence of random deception attacks and aperiodic Denial-of-Service (DoS) attacks. Based on the piecewise Lyapunov-Krasovskii function and decoupling method, a new secure synchronization criterion is proposed to realize the mixed H∞ and passive performance of CDNs against multiple attacks, and the control gain is gained. Lastly, the availability of the raised consequence is testified by two concrete examples.