Summary: In this paper, we consider numerical computations of invariant distributions for continuous-time Markov chains in terms of the censoring technique. Two basic properties are established for the censored continuous-time Markov chain that is viewed as a truncated augmentation approximation. Stable recursive formulas for continuous-time level-dependent M/G/1-type Markov processes are obtained, which are further applied to yield an effective algorithm for the invariant distribution of a generalized Markov branching process. Two examples are given to illustrate this algorithm.