Support matrix machine is an advanced matrix learning model that can fully utilize the intrinsic structural information in matrix data. However, it is susceptible to noise and outliers, and lacks generalization ability in imbalanced data. To this end, a robust cost-sensitive support matrix machine (RCSSMM) model is proposed and applied to intelligent diagnosis of wind turbine gearbox faults. RCSSMM improves the robustness to noise and outliers by evaluating the prior distribution of the matrix input with assembled matrix distance, and assigning different sample weights to different samples. Additionally, RCSSMM introduces the cost-sensitive loss function that assigns different penalty factors to different categories of matrix data. The optimal values of the penalty factors are adaptively determined with the Harris hawk optimization algorithm to focus on minority class samples and improve the diagnostic performance on imbalanced data. The proposed method is validated using simulated experimental data and real measured data of wind turbine gearboxes. The experimental results demonstrate that the RCSSMM model exhibits more outstanding fault diagnosis performance even under the presence of noise, outliers, and imbalanced data.