As shrinkage of transistors approaches its minimal limit, novel computing paradigms that keep evolvement of computer systems are essential. Representative example is a combinatorial problem solver based on Ising-model as an alternative for conventional software solvers running on a CPU. However, those hardware Ising machines still have limitation in their scalability and hence further breakthrough is mandatory for those machines to be applied to solve social scale problems. In this research, we aim to develop hardware-oriented algorithm to accelerate convergence of Ising-annealer by combining techniques derived from Markov chain Monte Carlo method and quantum annealing. We also design ASIC processors for demonstrating the performance of the algorithm.