On the basis of Huybrechts' weakly-coupling polaron model,the Tokuda modified linear-combination operator method and the unitary transformation method were used to study the properties of the weakly-coupling bound polaron considering an influence of Rashba effect,which is brought about by the spin-orbit(SO) interaction,in an semiconductor triangular quantum well(TQW).Numerical calculation on the GaAs triangular quantum well,as example,is performed.The expressions for the effective mass of the polaron as a function of the velocity and the coupling constant were derived.Numerical results show that the total effective mass of the polaron is composed of two parts.The interactions between the orbit and the spin with different direction have different effects on the effective mass of the polaron.