Effectively utilizing information from multiple sources and fewer labeled operating condition samples from a sucker-rod pumping system for oil production can improve the recognition effects and engineering practicability. Nevertheless, this is a challenging energy environment scientific application research subject, and therefore, this study proposes an operating state recognition scheme that relies on multisource nonlinear kernel learning and p-Laplacian high-order manifold regularization logistic regress. Specifically, three measured features are selected and extracted, i.e., wellhead temperature signal, electrical power signal, and ground dynamometer cards, based on mechanism analysis, expert experience, and prior knowledge. Finally, we establish the operating condition recognition model to recognize by the multisource p-Laplacian regularization kernel logistic regress algorithm. The experimental data are derived from 60 wells of a common high-pressure and low-permeability thin oil reservoir block of an oil field in China. The corresponding trials highlight that our scheme outperforms traditional recognition methods by exploiting single-source and multiple-feature data. In the context of fewer labeled samples, the proposed method has a greater recognition effect, engineering practicability, and better model robustness than the existing schemes based on other high-order manifold learning, verifying our method's effectiveness.