Accurate prediction of crude petroleum production in oil fields plays a crucial role in analyzing reservoir dynamics, formulating measures to increase production, and selecting ways to improve recovery factors. Current prediction methods mainly include reservoir engineering methods, numerical simulation methods, and deep learning methods, and the required prerequisite is a large amount of historical data. However, when the data used to train the model are insufficient, the prediction effect will be reduced dramatically. In this paper, a time series-related meta-learning (TsrML) method is proposed that can be applied to the prediction of petroleum time series containing small samples and can address the limitations of traditional deep learning methods for the few-shot problem, thereby supporting the development of production measures. The approach involves an architecture divided into meta-learner and base-learner, which learns initialization parameters from 89 time series datasets. It can be quickly adapted to achieve excellent and accurate predictions with small samples in the oil field. Three case studies were performed using time series from two actual oil fields. For objective evaluation, the proposed method is compared with several traditional methods. Compared to traditional deep learning methods, RMSE is decreased by 0.1766 on average, and MAPE is decreased by 4.8013 on average. The empirical results show that the proposed method outperforms the traditional deep learning methods.