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Predicting whether subjects with mild cognitive impairment (MCI) will convert to Alzheimer's disease is a significant clinical challenge. Longitudinal variations and complementary information inherent in longitudinal and multimodal data are crucial for MCI conversion prediction, but persistent issue of missing data in these data may hinder their effective application. Additionally, conversion prediction should be achieved in the early stages of disease progression in clinical practice, specifically at baseline visit (BL). Therefore, longitudinal data should only be incorporated during training to capture disease progression information. To address these challenges, a multi-view imputation and cross-attention network (MCNet) was proposed to integrate data imputation and MCI conversion prediction in a unified framework. First, a multi-view imputation method combined with adversarial learning was presented to handle various missing data scenarios and reduce imputation errors. Second, two cross-attention blocks were introduced to exploit the potential associations in longitudinal and multimodal data. Finally, a multi-task learning model was established for data imputation, longitudinal classification, and conversion prediction tasks. When the model was appropriately trained, the disease progression information learned from longitudinal data can be leveraged by BL data to improve MCI conversion prediction at BL. MCNet was tested on two independent testing sets and single-modal BL data to verify its effectiveness and flexibility in MCI conversion prediction. Results showed that MCNet outperformed several competitive methods. Moreover, the interpretability of MCNet was demonstrated. Thus, our MCNet may be a valuable tool in longitudinal and multimodal data analysis for MCI conversion prediction. Codes are available at https://github.com/Meiyan88/MCNET.