  Cram\'er's moderate deviations give a quantitative estimate for the relative
error of the normal approximation and provide theoretical justifications for
many estimator used in statistics. In this paper, we establish self-normalized
Cram\'{e}r type moderate deviations for martingales under some mile conditions.
The result extends an earlier work of Fan, Grama, Liu and Shao [Bernoulli,
2019]. Moreover, applications of our result to Student's statistic, stationary
martingale difference sequences and branching processes in a random environment
are also discussed. In particular, we establish Cram\'{e}r type moderate
deviations for Student's $t$-statistic for branching processes in a random
environment.
