Apicomplexan parasites cause diseases including malaria, toxoplasmosis, and babesiosis, affecting large parts of the world and hampering economic development to a considerable severity. Early recognition of pathogenic parasites can effectively constrain the spread of these infectious diseases. Recently, deep-learning-based computer-aided parasite recognition systems provide many practical tools for automated apicomplexan parasite recognition. However, existing research works are limited by the complicated and expensive manual annotating workload in supervised deep learning methods, which require many experts' manually annotated samples. Moreover, they also ignore the significance of correlations among different parasite cells, which retain helpful information for identification. Therefore, this paper is the first to employ a semi-supervised learning strategy to reduce the manual labeling workload and introduce a hybrid graph learning algorithm into parasite recognition. Our approach has a superior parasite recognition capability with semi-supervised techniques and the graph-based model. Specifically, this research proposes a Semi-Supervised Graph Learning (SSGL) framework, composing CNN (Convolutional Neural Networks) feature embedding, learnable graph building, and graph feature learning components. To verify the performance of the SSGL model, the paper applies multiple evaluation indicators to appraise our model, and the approach can achieve high accuracy of 91.75%, AUC of 91.83%, the sensitivity of 91.75% and specificity of 97.25% with only a small amount of labeled data (20%). In conclusion, SSGL model provides high parasite recognition capability with minimal labels, greatly reduces the workload of relevant experts, and promotes the popularization of computer-aided parasite diagnosis tools.