Exposure to air pollutants has become a major global health threat and is a dominant contributor to increasing respiratory mortality. Accurate projections of respiratory mortality are crucial to mitigating the adverse influences of air pollution on public health and guiding long-term policy implementation. However, the forecasting models' accuracy is difficult to guarantee because seasonal factors perturb the raw series of air pollutants and respiratory mortality. This paper proposes an enhanced seasonal and self-adaptive multivariate grey convolution model to solve this dilemma. The innovations of the proposed model reside in the following areas: firstly, a seasonal operator vector of multidimensional data is initially built to digitize the seasonality of air pollutants and related mortality. Secondly, a multivariate grey convolution model with an adaptive time-lag cumulative optimization item is put forward. The weight coefficients of each driving variable at different periods are intended to adapt dynamically. Thirdly, the self-adaptive time-delay coefficient is determined by the Particle Swarm Algorithm, enhancing the accuracy of predictions. Theoretically, the generalizability and adaptability of the newly presented model are well-validated. Moreover, its practical applicability and higher forecasting performance are further verified in estimating the respiratory mortality attributable to the comprehensive effects of air pollutants in China.