This paper proposes a novel hybrid model that integrates the synergy of two superior classifiers for functional magnetic resonance imaging (fMRI) recognition, namely, convolutional neural networks (CNNs) and support vector machines (SVMs), both of which have proven results in the field of image recognition. In the proposed model, the CNN functions as a trainable feature extractor and the SVM functions as a recognizer. This hybrid model extracts features from raw images and generates predictions for fMRI recognition. We conducted experiments on Haxby's 2001 fMRI dataset. Comparisons with Haxby's study using the same database indicated that the proposed fusion achieved superior recognition accuracy of 99.5% compared to the Haxby's approach. Further, when the CNN was used as a feature extractor, the SVM classifier was demonstrated to be the best combining counterpart, providing the best synergy effect in terms of accuracy. This is compared with other classifiers based on learning algorithms such as decision tree, neural network, K-nearest neighbor, random forest, and AdaBoost.