Strained-balanced In x Ga 1−x As/InAlAs quantum well structures have been shown to generate high carrier density, high-mobility layers suitable for power field effect transistor (FET) applications. Doped channel devices allow higher carrier densities than modulation-doped structures but with reduced carrier velocities due to increased ionized impurity scattering. The amount of ionized impurity scattering may be reduced by the introduction of compositional grading in In x Ga 1−x As quantum wells which results in an increasing depth of the quantum well on the opposite side to the delta-doped plane. The grading is achieved by the use of a number of steps, where each step has a fixed value of x. An ensemble Monte Carlo simulation has been used to calculate the velocity-field characteristics of the conduction electrons confined within the quantum well in such a structure. Here the envelope wavefunctions for the confined electrons are calculated using a self-consistent Poisson-Schrödinger solver. Our velocity-field characteristics show good agreement with experiment for the three-step structure but the agreement is noticeably worse for lattice-matched and five-step structures. We have shown that a correlation between the low-field mobility and saturation velocity observed experimentally for GaAs/AlGaAs and In x Ga 1−x As quantum wells and theoretically for GaAs/AlGaAs quantum wells is also valid for the predicted results in these structures. A similar explanation to that provided for the GaAs/AlGaAs quantum wells is shown to hold here.