In single-pixel imaging (SPI), the target object is illuminated with varying patterns sequentially and an intensity sequence is recorded by a single-pixel detector without spatial resolution. A high quality object image can only be computationally reconstructed after a large number of illuminations, with disadvantages of long imaging time and high cost. Conventionally, object classification is performed after a reconstructed object image with good fidelity is available. In this paper, we propose to classify the target object with a small number of illuminations in a fast manner for Fourier SPI. A naive Bayes classifier is employed to classify the target objects based on the single-pixel intensity sequence without any image reconstruction and each sequence element is regarded as an object feature in the classifier. Simulation results demonstrate our proposed scheme can classify the number digit object images with high accuracy (e.g. 80% accuracy using only 13 illuminations, at a sampling ratio of 0.3%).