In this paper, we consider the martingale Hardy spaces defined with the help of the mixed L p → -norm. Five mixed martingale Hardy spaces will be investigated: H p → s , H p → S , H p → M , P p → , and Q p → . Several results are proved for these spaces, like atomic decompositions, Doob's inequality, boundedness, martingale inequalities, and the generalization of the well-known Burkholder–Davis–Gundy inequality.