In variational data assimilation, traditional methods generally presuppose that both background errors and observation errors are distributed according to the Gaussian distribution. While this assumption simplifies mathematical operations and facilitates optimization, it demonstrates notable limitations in practical applications, particularly when dealing with non-Gaussian errors and outliers. This study proposes an innovative approach to constructing the objective function based on Kaniadakis entropy and the κ-generalized Gaussian distribution. The aim of this approach is to enhance the robustness of the 4-D variational data assimilation method. The incorporation of Kaniadakis entropy into the objective function effectively characterizes heavy-tailed error distributions, thereby significantly improving the suppression of outliers and observation errors and optimizing the stability of the assimilation process. The proposed method was validated using the Lorenz-63 model. The findings indicate that the objective function founded upon the κ-generalized Gaussian distribution attains a substantial diminution in root mean square error when processing observation data that encom-passes outliers. Furthermore, the assimilation results demonstrate enhanced stability and accuracy. This study provides a theoretical framework and methodological support for non-Gaussian error modeling and robust data assimilation, offering a novel perspective for data assimilation research in complex environments.