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 L_q-likelihood estimation (ML_qE) is a generalization of maximum likelihood estimation. Based on Fahrmeir et al, the weak consistency, strong consistency and asymptotic normality of the ML_qE 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 L_q-likelihood estimation is robust.