A new computing architecture, an annealing machine, is proposed. The annealing machine maps combinatorial optimization problems into an Ising model and solves the problems by its own convergence property．Several implementations of the annealing machine are proposed. One is a quantum annealing machine using superconductor devices. The other implementation is using optical devices and calculate the Ising model. We proposed a CMOS annealing machine, which is a ASIC/FPGA CMOS implementation of the annealing machines. We constructed prototypes of the CMOS annealing machine. The 1st generation prototype with ASIC implementation, the 2nd generation prototype with FPGA implementation and the card-size prototype with 2-chip ASIC implementation are used to confirm its ability to solve combinatorial optimization problems and its high energy efficiency. The 2nd and card-size prototypes also confirm its multiple-chip operation, which enables a higher scalability of the CMOS annealing machine solving large size optimization problems.