Cr-Si binary silicides are promising advanced functional materials, which are widely used in semiconductors, thermoelectric and high temperature industries. However, the correlation between structural feature and the overall properties of Cr-Si silicides are not unclear. Here, we apply the first-principles to study the structural, mechanical, electronic and thermodynamic properties of Cr-Si silicides. The result shows that one novel Cr2Si orthorhombic structure (Puma) is predicted. It is found that the calculated bulk modulus of Cr-Si silicides decreases with increasing Si concentration. The calculated shear modulus and Young's modulus of Cr3Si are larger than that of the other Cr-Si silicides because of the symmetrical Cr-Si bonds. However, Cr2Si shows better ductility and good plasticity in comparison to the other Cr-Si silicides. Compared to the CrSi2, these Cr-Si silicides show better electronic properties. Finally, it is found that the calculated Debye temperature (Theta(D)) of Cr-Si silicides obeys the sequence of Cr5Si3 >CrSi > Cr3Si > Cr2Si. Naturally, the high-temperature thermodynamic properties of Cr-Si silicides are attributed to the vibration of Si atom and Cr-Si bond. This work provides a theoretical framework for understanding the comprehensive properties of Cr-Si silicides and provides powerful guidelines for future improving the overall performances of Cr-Si silicides.