We study third-harmonic generation in a quantum well represented by a Poschl-Teller confining potential under an applied electric field. This potential is well suited for such purposes as it can easily become asymmetrical by a correct choice of its parameter set. We calculate the third harmonic generation within the density matrix formalism. Numerical results for a typical GaAs quantum well are presented. We investigate the third-harmonic generation for several values of asymmetry parameters under small electric fields. It is found to be enhanced with the increasing electric field. While the resulting third-harmonic generation peak is promising it is still quite smaller than that observed in similar quantum well systems. (C) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.