This paper deals with the robust control problem for a class of uncertain nonlinear networked systems with stochastic communication delays via sliding mode conception (SMC). A sequence of variables obeying Boulli distribution are employed to model the randomly occurring communication delays which could be different for different state variables. A discrete switching function that is different from those in the existing literature is first proposed. Then, expressed as the feasibility of a linear matrix inequality (LMI) with an equality constraint, sufficient conditions are derived in order to ensure the globally mean-square asymptotic stability of the system dynamics on the sliding surface. A discretetime SMC controller is then synthesized to guarantee the discrete-time sliding mode reaching condition with the specified sliding surface. Finally, a simulation example is given to show the effectiveness of the proposed method.