General-purpose Sparse Matrix-Matrix Multiplication (SpMM) is a fundamental kernel in scientific computing and deep learning. The emergence of new matrix computation units such as Tensor Cores (TCs) brings more opportunities for SpMM acceleration. However, in order to fully unleash the power of hardware performance, systematic optimization is required. In this paper, we propose Acc-SpMM, a high-performance SpMM library on TCs, with multiple optimizations, including data-affinity-based reordering, memory efficient compressed format, high-throughput pipeline, and adaptive sparsity-aware load balancing. In contrast to the state-of-the-art SpMM kernels on various NVIDIA GPU architectures with a diverse range of benchmark matrices, Acc-SpMM achieves significant performance improvements, on average 2.52x (up to 5.11x) speedup on RTX 4090, on average 1.91x (up to 4.68x) speedup on A800, and on average 1.58x (up to 3.60x) speedup on H100 over cuSPARSE.