Shubnikov-de Haas (S-dH) and Van der Pauw Hall effect measurements on a strained In0.15Ga0.85As/Al0.22Ga0.78As single quantum well grown by molecular beam epitaxy have been performed to demonstrate the existence of the two-dimensional electron gas in the In0.15Ga0.85As single quantum well. The results of the fast Fourier transform results for the S-dH data clearly indicate electron occupation of two subbands in the In0.15Ga0.85As single quantum well. Electronic subband energies and wavefunctions in the In0.15Ga0.85As quantum well were calculated by a self-consistent method taking into account exchange-correlation effects together without and with strain effects. The calculated total carrier density including the strain effect was in better agreements with that determined from the S-dH and Hall effect measurements.