We investigate the plasmon mode coupling and depolarization shifts in AlGaAs/GaAs asymmetric step quantum wells (ASQWs) of the two-subband model with the Bohm–Pine’s random-phase approximation with and without an applied electric field. By adjusting the well geometry parameters and material composition systematically, various characteristics of plasmons in ASQWs are found for different asymmetric cases. We find that (i) the intersubband plasmon has a large negative dispersion in long wavelength limit; (ii) the step width related depolarization shift depends on the number of subbands in the deep well; and (iii) the influence of electric field effect on depolarization shift and the coupling of the two plasmon modes is quite asymmetric with its minimum at +8 kV/cm by changing the electrical field and the ASQW structure parameters. The coupling and decoupling of the intersubband and intrasubband plasmon modes can be realized by adjusting the polarity and the strength of the external electric field and changing the ASQW structure parameters.