Under the dipole approximation,based on the Fermi Golden Rule,longit udinal optical (LO) phonons spontaneous emission rate in the two-parameter asy m metric Gauss potential quantum dot is investigated by using the Lee-Low-Pine u ni tary transformation and Pekar-type transformation variational method.Numerical results show that the spontaneous emission rate will decreases with increasing t he electron -phonon coupling strength and the dispersion coefficient,and will i ncreases with increasing the well depth of the asymmetric Gauss potential;the s pontaneous emission rate changes with the well width of the asymmetric Gauss pot ential as a asymmetric "Gaussian distribution" and are significantly affected by the electron -phonon coupling strength,the dispersion coefficient and the wel l depth of asymmetric Gauss potential;selecting two-parameter asymmetric Gauss p otential to describe the confinement effects of electrons in quantum dot can ref lect more quantization characteristics of phonon spontaneous emission rate,whil e the single-parameter parabolic potential approximation of the asymmetric Gaus s potential gives simple and rough results.The influence of the dispersion and t he electron -phonon coupling strength of the materials on the LO spontaneous em i ssion rate in the two-level system cannot be ignored.The results of this paper will help reveal the effects of phonon on the optoelectronic and transport prope rties of quantum dot.