Cloud-native databases have been widely deployed due to high elasticity, high availability and low cost. However, most existing cloud-native databases do not support multiple writers and thus have limitations on write throughput and scalability. To alleviate this limitation, there is a need for multi-primary databases which provide high write throughput and high scalability. In this paper, we present a cloud-native multi-primary database, GaussDB, which adopts a three layer (compute-memory-storage) disaggregation framework, where the compute layer is in charge of transaction processing, the memory layer is responsible for global buffer management and global lock management, and the storage layer is used for page and log persistence. To provide multi-primary capabilities, GaussDB logically partitions the pages to different compute nodes and then assigns the ownership of each page to a compute node. For each transaction posed to a compute node, if the compute node owns all relevant pages of this query, the compute node can process the query locally; otherwise, GaussDB transfers the ownership of relevant pages to this node. To capture data affinity and reduce page transmission costs, GaussDB designs a novel page placement and query routing method. To improve recovery performance, GaussDB employs a two-tier (memory-storage) checkpoint recovery method which uses memory checkpoints combined with on-demand page recovery to significantly improve recovery performance. We have implemented and deployed GaussDB internally at Huawei and with customers, and the results show that GaussDB achieves higher throughput, lower latency, and faster recovery than state-of-the-art baselines.