Abstract: Introducing power-to-hydrogen（PtH） into offshore wind farms can assist the integration of wind power and produce green hydrogen, which accelerates decarbonization in industrial sectors and has attracted attention worldwide. In these circumstances, this paper studies the real-time energy management strategy of the offshore wind PtH microgrid. First, the real-time energy management model of the offshore wind PtH microgrid is proposed, including offshore wind farms, PtH devices and hydrogen storage tanks. Then, real-time energy management strategy based on approximate dynamic programming（ADP） is proposed. The value function is approximated by piece-wise linear functions（PLFs） to cope with uncertainties in the microgrid. Finally, the effectiveness and superiority of the proposed strategy is verified by case studies. Under the proposed strategy, offshore wind power can be consumed by PtH, achieving production and storage of hydrogen in advance. On the basis of the ideal case with perfect forecasting, the proposed strategy has an average optimization accuracy of more than 99% in real-time test scenarios with normal distribution.