Due to completely open-air operation, fog-haze has become the main cause of contamination on the insulator surface of overhead contact lines (OCLs), further leading to pollution flashover and a series of serious risk consequences. To perceive the fog-haze-caused pollution flashover (FHPF) risk of OCL insulator, a robust deep Gaussian process (DGP)-based uncertainty-aware trustworthy prediction approach is proposed, incorporating epistemic and aleatoric uncertainties. In particular, aiming at the imbalanced dataset with limited fault samples, the prediction of FHPF risk is cast as a classification problem, and solved by DGP using stochastic gradient Hamiltonian Monte Carlo (SGHMC) inference. The key parameters are identified investigating the influences of fog-haze on insulator surface contamination. Furthermore, the SGHMC sampling-based inference is utilized to efficiently capture the intractable posterior distribution, dealing with uncertainty and enhancing the flexibility of the prediction approach. Finally, extensive experiments on high-speed railway line validate the effectiveness and superior of the proposed approach, compared to other advanced predictive classification methods. In addition, it cannot only capture the prediction uncertainty over a limited number of fault samples, but also achieve favorable prediction performance under unseen noisy environments, ultimately ensuring robust and trustworthy FHPF risk predictions for OCLs.