We consider the stabilization problem for a class of networked control systems in the discrete-time domain with random delays. The sensor-to-controller and controller-to-actuator delays are modeled as two Markov chains, and the resulting closed-loop systems are jump linear systems with two modes. The necessary and sufficient conditions on the existence of stabilizing controllers are established. It is shown that state-feedback gains are mode-dependent. An iterative linear matrix inequality (LMI) approach is employed to calculate the state-feedback gains.