The spin splitting of the Al x Ga 1 À x As/GaAs/Al y Ga 1 À y As/Al x Ga 1 À x As (x a y) step quantum wells (QWs) is theoretically investigated by the method of finite difference. The Al concentration in the barrier and in the step can dramatically affect the Rashba spin splitting induced by the internal structure inversion asymmetry of the step QWs, the Dresselhaus spin splitting and the anisotropy of the total spin splitting. The Rashba spin splitting of the step QWs with AlAs barrier, which is nearly 2 meV, is much larger than that of the step QWs with the Al x Ga 1 À x As ðx o 0:4Þ barrier. The Al concentration in the step plays different role on the spin splitting of the step QWs with AlAs barrier and Al x Ga 1 À x As barrier. The cooperation of the Al concentration in the barrier and in the step determines which effect, Rashba or Dresselhaus, dominates the total spin splitting. For the step QWs with AlAs barrier, which effect is the dominating one depends on the Al concentration in the step. For the step QWs with Al x Ga 1 À x As barrier, the Dresselhaus effect gives a significant contribution to the total spin splitting without electric field.