The metering accuracy of capacitive voltage transformers (CVTs) affects the fairness of electricity settlement, and the online measurement of their metering errors has become a research hotspot. This error consists of amplitude and phase errors of three-phase voltages. In this paper, because the error data is characterized by time series, nonlinearity, and large volumes, the Gate recurrent unit is selected as a deep learning framework to predict it, the Batch normalization is proposed to prevent gradient disappearance, and the self-attentive mechanism is proposed to help learn long-time information. To measure all six errors simultaneously, multitask learning is employed to mine the shared information and coupling among multiple tasks, and the loss function is reconstructed to ensure simultaneous convergence of the six tasks. Experimental results show that, compared with the traditional single-task model, the accuracy indexes MSE, RMSE, and MAE of the proposed model are reduced by 95.1%, 81.1%, and 89.5% on average for all tasks, and the total training time is reduced by 57.8%; compared with other multitask models, the accuracy indexes are improved by orders of magnitude. This shows that the proposed model fully meets the requirements of both accuracy and speed for online measurement of CVT error.