We present a rapid label-free imaging flow cytometry and cell classification approach based directly on raw digital holograms. Off-axis holography enables real-time acquisition of cells during rapid flow. However, classification of the cells typically requires reconstruction of their quantitative phase profiles, which is time-consuming. Here, we present a new approach for label-free classification of individual cells based directly on the raw off-axis holographic images, each of which contains the complete complex wavefront (amplitude and quantitative phase profiles) of the cell. To obtain this, we built a convolutional neural network, which is invariant to the spatial frequencies and directions of the interference fringes of the off-axis holograms. We demonstrate the effectiveness of this approach using four types of cancer cells. This approach has the potential to significantly improve both speed and robustness of imaging flow cytometry, enabling real-time label-free classification of individual cells.