The properties of bound magnetopolaron, which is weakly coupled to LO-phonon in an asymmetric quantum dot (QD) were studied by using Tokuda modified linear combination operator and unitary transformation methods. The expression of ground-state energy as functions of the transverse and longitudinal confinement lengths and magnetic field was derived. After a simple numerical calculation, it’s found that the ground-state energy of bound magnetopolaron splits into two branches after taking the spin influence into account. The ground-state energy and spin-up(down) splitting energy decrease with increasing the transverse and longitudinal confinement lengths, and they are increasing functions of magnetic field.