By using Huybrechts′ linear combination operator and the second Lee-Low-Pines (LLP) unitary transformation method, the properties of the strong-coupling polaron in RbCl asymmetrical semi-exponential quantum well are investigated. The vibrational frequency and ground state energy of the strong-coupling polaron in a RbCl asymmetrical semi-exponential quantum well are obtained, and the variation of the vibrational frequency and ground state energy with the two positive parameters (U0 and σ) of the asymmetrical semi-exponential confinement potential is derived theoretically. RbCl crystal material is selected for numerical calculation, and the results indicate that U0 and σ are important physical quantities for investigating the properties of the strong-coupling polaron in asymmetrical semi-exponential quantum well, and the vibrational frequency and ground state energy of the strong-coupling polaron increase with the increase of U0, while decrease with the increase of σ.