In this paper, on the basis of Huybrechs' strong-coupled polaron model, the Tokuda-modified linear-combination operator method and the unitary transformation method are used to study the properties of the strong-coupled bound polaron considering the influence of Rashba effect, which is brought by the spin-orbit (SO) interaction, in an asymmetric quantum dot (QD). The expression for the effective mass of the polaron as functions of the transverse and longitudinal bound strengths, velocity, vibration frequency, and the bound potential has been derived. After a simple numerical calculation on the RbCl crystal, we found that the total effective mass of the bound polaron is composed of three parts. The interaction between the orbit and the spin with different directions has different effects on the effective mass of the bound polaron.