Abstract: Reproductive dispersion linear models (RDLMS) are the natural generalization of statistical models such as linear regression models, generalized linear models and exponential linear models. Maximum Lq-likelihood estimation (MLqE) is a generalization of maximum likelihood estimation. Based on Fahrmeir et al, the weak consistency, strong consistency and asymptotic normality of the MLqE of RDLMS are obtained, and the existing conclusions are generalized. Finally, a simulation example is given. The results show that our estimation method is effective and the maximum Lq-likelihood estimation is robust.