Existing cross-modal pedestrian re-identification methods disregard noise interference and valuable information for pedestrian identification in modal specific features. Hence, a cross-modal pedestrian re-identification network combining frequency-domain attention and modal co-feature optimization is proposed to effectively suppress noise interference in different modal spaces and deeply mine and utilize the implicit identity-discrimination informations in modal specific features. First, a two-stream network integrated with a frequency-domain attention mechanism is used to effectively filter noise and extract modal shared and specific features. Second, the extracted modal specific features are purified and restored to reduce modal-style differences, while identity-discrimination informations are extracted and strengthened independent of modalities. Thereafter, this implicit discrimination informations are used to guide modal shared features to enhance the model's recognizability. Finally, variance aggregation loss is introduced to minimize the modal differences among the enhanced modal shared features. Based on extensive experimental results, the proposed method demonstrates significant performance improvement on three public datasets. In particular, its Rank-1 accuracy and mean average precision are 82.14% and 81.59%, respectively, in the all-search mode on the SYSU-MM01 dataset.