Jacobi computation is a kind of stencil computation, which has been widely applied in the field of scientific computing. The performance optimization of Jacobi computation is a classic topic, where loop tiling is an effective optimization method. The existing loop tiling methods mainly focus on the impact of tiling on parallel communication and program locality and fail to consider other factors such as load balancing and vectorization. This study analyzes and compares several tiling methods based on multi-core computing architecture and chooses an advanced hexagonal tiling as the main method to accelerate Jacobi computation. For tile size selection, this study proposes a hexagonal tile size selection algorithm called Hexagon_TSS by comprehensively considering the impact of tiling on load balancing, vectorization efficiency, and locality. The experimental results show that the L1 data cache miss rate can be reduced to 5.46% of original serial program computation in the best case by Hexagon_TSS, and the maximum speedup reaches 24.48. The proposed method also has excellent scalability.