With the continuous expansion of the scale of optical communication network and the rapid increase of network traffic demand, the management form of multi-domain optical network has widely existed. OSNR is an important indicator to judge the quality of communication. It is very important to predict OSNR more accurately in a low-cost and energy-saving way in multi-domain optical networks. In this paper, a scheme of federal learning in multi-domain optical networks is proposed to improve the accuracy of the OSNR prediction. The main idea is to train hybrid machine learning model in each single domain, then the strategy of federal learning is used for optimization it in multi-domains. The performance of the proposed scheme is verified by simulation experiments. The strategy can alleviate the problems of data silos and model training set caused by multi-domain optical network. According to simulation result, when the amount of data reaches 5×103, adding this strategy will reduce the mean square error of the prediction model by about 18%. It can improve the performance of machine learning model, the ability of OSNR prediction and the reliability of network operation.