The improvement in overall properties is a big challenge for the development of high-temperature materials. The refractory Al-rich MoAl 5 is a potential high temperature alloy due to the excellent oxidation resistance and high mechanical properties. However, the correlation between structural and overall properties of MoAl 5 is unclear. In this work, the structural stability, elastic and thermodynamic properties of MoAl 5 are studied by the first-principles calculations. Two phases: hexagonal and cubic structures, are considered. The result shows that the hexagonal MoAl 5 is a table phase. Compared to the cubic MoAl 5 , the hexagonal MoAl 5 exhibits high bulk modulus, shear modulus and Young modulus due to the strong localized hybridization between Mo and Al. Here, it is found that the calculated bulk modulus, shear modulus and Young modulus of the hexagonal MoAl 5 are 119, 98 and 230GPa. Finally, the high temperature thermodynamic properties of MoAl 5 are related to the vibration of Al atom and Al-Mo bond, which is demonstrated by the density of state and chemical bonding.