GPUs are being applied widely to batch workloads that benefit from the parallel processing capabilities of GPUs. To enable the processing of concurrent batch-based transactions on GPUs, existing systems build dependency graphs during a pre-execution phase to manage read and write operations. However, as dependency-graph maintenance introduces a sub-stantial overhead, there is a need for more efficient transaction support to exploit the power of GPUs more fully for transaction processing. This paper proposes LTPG, a novel GPU-enabled database system that offers increased versatility and efficiency by eliminating the need for predefined read/write-sets. LTPG employs deterministic optimistic concurrency control to ensure correct transaction execution, thus avoiding the maintenance of dependency graphs. The proposed concurrency control simpli-fies transaction processing workflows and avoids the overhead associated with managing dependency graphs, thus resulting in improved efficiency. LTPG divides a workflow into three stages: execution, conflict detection, and write-back, leveraging the parallelism of GPUs. Moreover, several additional optimization strategies are adopted to improve system performance. Experiments with real-world workloads from two benchmarks verify LTPG can achieve effective improvement in the throughput and latency compared to the leading baselines.