The generalized master equation for the space-time coupled continuous time random walk is derived analytically,in which the space-time coupling is considered through the correlated function g(t) ～ tγ,0 ≤ γ ＜ 2,and the probability density function ω(t) of a particle’s waiting time t follows a power law form for large t:ω(t) ～ t-(1 +α),0 ＜ α ＜ 1.The results indicate that the expressions of the generalized master equation are determined by the correlation exponent γ and the long-tailed index α of the waiting time.Moreover,the diffusion results obtained from the generalized master equation are in accordance with the previous known results and the numerical simulation results.