Alzheimer's disease (AD) is an incurable neurodegenerative condition leading to cognitive and functional deterioration. Given the lack of a cure, prompt and precise AD diagnosis is vital, a complex process dependent on multiple factors and multi-modal data. While successful efforts have been made to integrate multi-modal representation learning into medical datasets, scant attention has been given to 3D medical images. In this paper, we propose Contrastive Masked Vim Autoencoder (CMViM), the first efficient representation learning method tailored for 3D multi-modal data. Our proposed framework is built on a masked Vim autoencoder to learn a unified multi-modal representation and long-dependencies contained in 3D medical images. We also introduce an intra-modal contrastive learning module to enhance the capability of the multi-modal Vim encoder for modeling the discriminative features in the same modality, and an inter-modal contrastive learning module to alleviate misaligned representation among modalities. Our framework consists of two main steps: 1) incorporate the Vision Mamba (Vim) into the mask autoencoder to reconstruct 3D masked multi-modal data efficiently. 2) align the multi-modal representations with contrastive learning mechanisms from both intra-modal and inter-modal aspects. Our framework is pre-trained and validated ADNI2 dataset and validated on the downstream task for AD classification. The proposed CMViM yields 2.7\% AUC performance improvement compared with other state-of-the-art methods.