In this paper, the problem of control algorithm design for a class of nonlinear two-input and two-output (TITO) networked control systems (NCSs) with non-Gaussian random time delays is investigated, where a general non-linear auto-regressive moving average with exogenous model is used to describe the plant. Due to the non-Gaussian random time delays involved in the systems, it is insufficient to obtain a satisfactory optimal control algorithm by only controlling the expected value of the tracking errors. The Renyi entropies of the tracking errors and control inputs are adopted to characterize the randomness of the closed-loop system. The formulations of the probability density functions (PDFs) of the tracking errors and control inputs are deduced. By minimizing the new performance index, a recursive optimal control algorithm is obtained. Furthermore, the local stability condition of the closed-loop systems is established. Finally, the simulation results are presented to illustrate the effectiveness of the proposed method.