Photonic neural networks are brain-inspired information processing technology using photons instead of electrons to perform artificial intelligence (AI) tasks. However, existing architectures are designed for a single task but fail to multiplex different tasks in parallel within a single monolithic system due to the task competition that deteriorates the model performance. This paper proposes a novel optical multi-task learning system by designing multi-wavelength diffractive deep neural networks (D2NNs) with the joint optimization method. By encoding multi-task inputs into multi-wavelength channels, the system can increase the computing throughput and significantly alle-viate the competition to perform multiple tasks in parallel with high accuracy. We design the two-task and four-task D2NNs with two and four spectral channels, respectively, for classifying different inputs from MNIST, FMNIST, KMNIST, and EMNIST databases. The numerical evaluations demonstrate that, under the same network size, mul-ti-wavelength D2NNs achieve significantly higher classification accuracies for multi-task learning than single-wavelength D2NNs. Furthermore, by increasing the network size, the multi-wavelength D2NNs for simultaneously performing multiple tasks achieve comparable classification accuracies with respect to the individual training of multiple single-wavelength D2NNs to perform tasks separately. Our work paves the way for developing the wave-length-division multiplexing technology to achieve high-throughput neuromorphic photonic computing and more general AI systems to perform multiple tasks in parallel.