We calculated the drift-velocities of electrons and holes of I $n_{0.53}$(A $l_{x}$G $a_{1-x}$ )$_{0.47}$As, which is used for semiconductor materials of high performance HBTs, along with the various doping concentrations and Al mole fractions as well as the electric fields by Monte Carlo experiment. Especially, for the valence bands the accuracy of hole-drift-velocity was improved in the consideration of intervalley scattering due to the inelastic scattering of acoustic phonon. From the results the empirical formulas of the low- and high field mobility of electrons and holes were extracted by using nonlinear least square fitting method. The accuracy of the formulas was proved by comparing the formula of low-field electron mobility as well as drift-velocity of I $n_{0.53}$ G $a_{0.47}$As and of low-field hole mobility of GaAs with the measured values, where the error was below 10%. For the high-field mobilities of electron and hole the results calculated by the formulas were very well matched with the MC experimental results except at the narrow field range where the electrons produced the velocity overshoot and the corresponding error was about 30%.0%. 30%.0%.