Continuous Sign Language Recognition (CSLR) is a task which converts a sign language video into a gloss sequence. The existing deep learning based sign language recognition methods usually rely on large-scale training data and rich supervised information. However, current sign language datasets are limited, and they are only annotated at sentence-level rather than frame-level. Inadequate supervision of sign language data poses a serious challenge for sign language recognition, which may result in insufficient training of sign language recognition models. To address above problems, we propose a cross-modal knowledge distillation method for continuous sign language recognition, which contains two teacher models and one student model. One of the teacher models is the Sign2Text dialogue teacher model, which takes a sign language video and a dialogue sentence as input and outputs the sign language recognition result. The other teacher model is the Text2Gloss translation teacher model, which targets to translate a text sentence into a gloss sequence. Both teacher models can provide information-rich soft labels to assist the training of the student model, which is a general sign language recognition model. We conduct extensive experiments on multiple commonly used sign language datasets, i.e., PHOENIX 2014T, CSL-Daily and QSL, the results show that the proposed cross-modal knowledge distillation method can effectively improve the sign language recognition accuracy by transferring multi-modal information from teacher models to the student model. Code is available at https://github.com/glq-1992/cross-modal-knowledge-distillation_new.