An optical-electronic hybrid convolutional neural network (CNN) system is proposed and investigated for its parallel processing capability and system design robustness. It is regarded as a practical way to implement real-time optical computing. In this paper, we propose a complex-valued modulation method based on an amplitude-only liquid-crystal-on-silicon spatial light modulator and a fixed four-level diffractive optical element. A comparison of computational results of convolutions between different modulation methods in the Fourier plane shows the feasibility of the proposed complex-valued modulation method. A hybrid CNN model with one convolutional layer of multiple channels is proposed and trained electrically for different classification tasks. Our simulation results show that this model has a classification accuracy of 97.55% for MNIST, 88.81% for Fashion MNIST, and 56.16% for Cifar10, which outperforms models using only amplitude or phase modulation and is comparable to the ideal complex-valued modulation method.