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The modelling and control problems are studied for a class of networked control systems (NCSs) with both network-induced delays and random packet losses. The packet-loss processes in the forward channel and the backward channel are modelled as two Markov chains. The state feedback control law is considered, and the resulting closed-loop system is a discrete-time Markovian linear system with two modes. Mean-square exponential stability conditions are derived for the closed-loop NCS by using a properly constructed Lyapunov function. Corresponding state feedback controllers design procedures are also presented based upon the stability conditions. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method.