A security control problem is addressed for a kind of networked Markov jump system subject to two-side stochastic denial-of-service (DoS) attacks, in which the attack occurrence situation obeys the Markov chain. To resist the attack effects, a redundant channel protocol is adopted, wherein measurement/control signals are sent to the controller/actuator via the redundant channel when the primary channel suffers from cyber-attacks. According to the above redundant channel protocol, both measurement and input models are established to represent the received signals by the controller and actuator, respectively. Then, a novel two-layer mapping strategy via logical operations is proposed to describe attack occurrences and system jumping. These facilitate the design of a security sliding mode controller, under which the exponential mean-square stability of the networked Markov jump systems subject to DoS attacks and the corresponding sufficient conditions are derived. Eventually, the simulation results via the DC chopper circuit system are provided to illustrate the proposed redundant-channel-based security control method.