Multinational enterprises conduct global business that has a demand for geo-distributed transactional databases. Existing state-of-the-art databases adopt a sharded master-follower replication architecture. However, the single-master serving mode incurs massive cross-region writes from clients, and the sharded architecture requires multiple round-trip acknowledgments (e.g., 2PC) to ensure atomicity for cross-shard transactions. These limitations drive us to seek yet another design choice. In this paper, we propose a strongly consistent OLTP database GeoGauss with full replica multi-master architecture. To efficiently merge the updates from different master nodes, we propose a multi-master OCC that unifies data replication and concurrent transaction processing. By leveraging an epoch-based delta state merge rule and the optimistic asynchronous execution, GeoGauss ensures strong consistency with light-coordinated protocol and allows more concurrency with weak isolation, which are sufficient to meet our needs. Our geo-distributed experimental results show that GeoGauss achieves 7.06X higher throughput and 17.41X lower latency than the state-of-the-art geo-distributed database CockroachDB on the TPC-C benchmark.