Poor working condition makes internal pump leakage become one of the most frequent faults of hydraulic systems in industrial and agricultural production. The faults detection of the internal pump leakage not only suffers from the feature engineering but also the data acquisition and transmission. The latter may lead to the highly (over 50%) incomplete data problem which is deadly for fault diagnosis. Hence, the highly incomplete data problem is defined in this study. Then a two-stage fault diagnosis method based on the flow data is proposed. In the first stage, a Denoising Auto-Encoder with the conditional mask is used to complement the incomplete flow data. The conditional mask helps the model get extra information at a high missing ratio. In the second stage, with the help of masked noise and the Mask Attention mechanism, a classifier orients to the completed data is trained. These modifications help the classifier pay more attention to the remaining parts of flow data. The proposed method achieves the accuracy of 97% and 96% on the flow data which is missing by 60% and 70%. All the improvement measures are justified by the ablation and comparison experiments.