We investigated the drift and diffusion dynamics of spin wave packets under spin-orbit effective magnetic fields in two-dimensional electron systems. A simplified model with a spin drift-diffusion equation predicted that the spin phase velocity will change over time from a large negative value to a small positive value. Kerr rotation microscopy revealed the trend we expected for the phase velocity in spin wave packets in a GaAs quantum well. Monte-Carlo simulations agreed with the experiment and showed that the phase velocity can be simply characterized by the spin- orbit parameters and the size ratio between the instantaneous and initial wave packets. (C) 2018 The Japan Society of Applied Physics