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We give a Cram\'{e}r moderate deviation expansion for martingales withdifferences having finite conditional moments of order $2+\rho, \rho \in(0,1],$ and finite one-sided conditional exponential moments. The upper boundof the range of validity and the remainder of our expansion are both optimal.Consequently, it leads to a "half-side" moderate deviation principle formartingales. It is worth mentioning that our result is new even for independentrandom variables. Moreover, applications to quantile coupling inequality,$\beta$-mixing and $\psi$-mixing sequences are discussed.

Cram\'{e}r moderate deviation expansion for martingales with one-sided Sakhanenko's condition and its applications