As a fundamental factorization operation, the singular value decomposition (SVD) plays a paramount role in a broad range of domains such as scientific computing and machine learning. Due to its computational bottleneck of factorization for small matrices in real-world applications, many GPU-accelerated batched SVD algorithms have been investigated recently. However, these algorithms failed to achieve a balance between data locality and parallelism because their workflows depend on the size of each matrix. In this work, we propose a matrix-size-independent W-cycle algorithm to accelerate the batched one-side Jacobi SVD on GPUs, which successfully strikes the balance between data locality and parallelism. The experimental evaluation demonstrates that the proposed algorithm achieves $4.5 \times$ performance speedup on average over the state-of-the-art cuSOLVER.