This talk concerns with the computation of zero-sum stochastic games with the risk-sensitive average criterion. First, we establish the existence of the value and a saddle point under a mild condition，which is weaker than those in [SIAM J. Control Optim. 2019, 57(1): 219-240] and [Stochastic Process. Appl. 2014, 124(1): 961-983]. Next, different from the existing literature on the risk-sensitive average stochastic games which only focuses on the existence of saddle points, we additionally propose two algorithms to approximate the value and saddle points, respectively. Finally, we give an example to illustrate our conclusions.