We　focus　on　in　this　paper　the　convergence　rate　of　the　L-N　estimators　for　the　fixed　effect　β　in　Poisson-Gamma　models　which　are　typical　hierarchical　generalised　linear　models(HGLMs).　Under　the　proper　assumptions　on　response　variables　and　some　smoothing　conditions,　we　obtain　the　strong　consistency　and　the　convergence　rate　of　the　L-N　estimator　based　on　the　combination　of　L-N　and　quasi-likelihood.　©　2006　Springer-Verlag　Berlin　Heidelberg.