(1) Background: People may be infected with an insect-borne disease (malaria) through the blood input of malaria-infected people or the bite of Anopheles mosquitoes. Doctors need a lot of time and energy to diagnose malaria, and sometimes the results are not ideal. Many researchers use CNN to classify malaria images. However, we believe that the classification performance of malaria parasites can be improved. (2) Methods: In this paper, we propose a novel method (ROENet) to automatically classify malaria parasite on the blood smear. The backbone of ROENet is the pre-trained ResNet-18. We use randomized neural networks (RNNs) as the classifier in our proposed model. Three RNNs are used in ROENet, which are random vector functional link (RVFL), Schmidt neural network (SNN), and extreme learning machine (ELM). To improve the performance of ROENet, the results of ROENet are the ensemble outputs from three RNNs. (3) Results: We evaluate the proposed ROENet by five-fold cross-validation. The specificity, F1 score, sensitivity, and accuracy are 96.68 ± 3.81%, 95.69 ± 2.65%, 94.79 ± 3.71%, and 95.73 ± 2.63%, respectively. (4) Conclusions: The proposed ROENet is compared with other state-of-the-art methods and provides the best results of these methods.