In the current study, the linear combination operator (LCO) and Lee–Low–Pines unitary transformation (LLPUT) are adopted to verify the effect of the anisotropic parabolic potential (APP) on the polaron’s properties in the asymmetric Gaussian quantum well (AGQW). Relations of the vibrational frequency (VF) and the ground state energy (GSE) of weak coupling polaron in the AGQW for GaAs crystal varying with the effective confinement strengths of the APP, the barrier height, and range of the asymmetric Gaussian confinement potential (AGCP) are derived. The numerical calculated results illustrate that the GSE and VF of the weak coupling polaron in the AGQW can increase according to the effective confinement strengths’ growth for given values of the barrier height and range of the AGCP. They will increase by increasing the barrier height of the AGCP. However, they are decreasing functions of the range of the AGCP for the determined values of the effective confinement strengths and the barrier height of the AGCP.