The pre-trained language model has been developed for evaluating the quality of machine translation. It achieves state-of-the-art results. However, building a model for the evaluation of machine translation still faces the following challenges: 1) large scale of the training data affects the speed of the optimization; 2) the varied quality of the training data makes the optimization process unstable. To alleviate the issues of data learning, curriculum learning is proposed to rearrange the training sequence following an 'easy-to-hard' process. However, the definition of difficulty can not be directly applied to the training data used in the machine translation evaluation. Hence, we propose an obscurity-quantified curriculum learning framework for this task. Specifically, the obscurity of each training example can be measured from multiple perspectives, including the difficulty of ranking, the fuzziness of reference, the complexity of text, and the unreliability of judgement. To incorporate the obscurity measurements, we also design a dynamic learning strategy to guide the training process from instances with low obscurity to those with high-obscurity. Experimental results show that our proposed methods yield remarkable improvements on the segment-level WMT2019 and WMT2020 Metrics Shared Tasks compared to other baseline methods.