The taxonomic composition and abundance of phytoplankton have a direct impact on marine ecosystem dynamics and global environment change. Phytoplankton classification is crucial for phytoplankton analysis, but it is challenging due to their large quantity and small size. Machine learning is the primary method for automatically performing phytoplankton image classification. As large-scale research on marine phytoplankton generates overwhelming amounts of data, more powerful computational resources are required for the success of machine learning methods. Recently, quantum machine learning has emerged as a potential solution for large-scale data processing by harnessing the exponentially computational power of quantum computers. Here, for the first time, we demonstrate the feasibility of using quantum deep neural networks for phytoplankton classification. Hybrid quantum-classical convolutional and residual neural networks are developed based on the classical architectures. These models strike a balance between the limited function of current quantum devices and the large size of phytoplankton images, making it possible to perform phytoplankton classification on near-term quantum computers. Our quantum models demonstrate superior performance compared to their classical counterparts, exhibiting faster convergence, higher classification accuracy and lower accuracy fluctuation. The present quantum models are versatile and can be applied to various tasks of image classification in the field of marine science.