In the current research, the impacts of anisotropic parabolic confinement potential (APCP) on strong-coupled impurity bound magnetopolaron (SCIMP) in asymmetrical semi-exponential quantum wells (ASEQWs) containing hydrogen-like impurities (HLIs) at their center under uniform magnetic fields applied along the direction of z axis have been theoretically investigated. Lee-Low-Pine unitary transformation and linear combination operation methods were applied for the derivation of formulations for ground state energy (GSE) and the mean number of LO phonons (MNLOP) of SCIMPs. Also, GSE and MNLOP as functions of magnetic field cyclotron frequency, Coulombic impurity potential (CIP) strength, APCP effective confinement strengths along x and y directions, and two positive parameters of asymmetrical semi-exponential confinement potential (ASECP) were acquired. Numerical results were expressed for a typical CsI. It was found that when considering magnetic field, APCP, CIP, ASECP, GSE and MNLOP were increased.