Cramer's moderate deviations give a quantitative estimate for the relative error of the normal approximation and provide theoretical justifications for many estimators used in statistics. In this talk, we present a self-normalized Cramer type moderate deviations for martingales under some mild conditions. Moreover, applications of our result to Student's statistic, stationary martingale difference sequences and branching processes in a random environment are also discussed. The talk is based on some join works with Qi-Man Shao.