Abstract: Considering the randomness of offshore wind power and the increasingly prominent environmental problems, we propose a low-carbon distributionally two-stage robust optimization model considering conditional value at risk(CVaR) for hybrid AC/DC grids after taking the voltage source converter high voltage direct current (VSC-HVDC) as research object. In order to consider the uncertainty of probability distribution and the tail risk of the extreme scene, we build a fuzzy set of probability distribution by kullback-leibler divergence (KL) and utilize the CVaR to quantify the tail loss of the extreme scene in the worst probability distribution. Furthermore, by adopting the ladder-type carbon trading and rationally utilizing the flexible resources and energy storage devices, not only the flexibility of the system operation is enhanced but also the carbon emissions are reduced on the premise of operational risks. In order to improve the calculation speed, a double-cycle decomposition method is proposed based on the column-and-constraint generation method (C&CG) and Multi-cut benders decomposition method. Finally, the effectiveness of the proposed model and algorithm is verified by the modified IEEE RTS 79 tested system.