<p>The minimum dominating set (MDS) problem is a well-known NP-hard problem in graph theory. While several quantum algorithms have been proposed to address this problem, their implementation typically requires a large number of qubits, which poses a significant challenge for noisy intermediate-scale quantum (NISQ) devices. In this study, we introduce a quantum algorithm based on the quantum alternating operator ansatz (QAOA+) to solve the MDS problem. We design a mixing operator that can effectively explore feasible dominating sets. A key challenge, however, is building a quantum circuit corresponding to this mixing operator. To address this, we extend the controlled-bit-flip mixer (CBFM) to the Boolean-variables controlled-bit-flip mixer (BV-CBFM) and provide some building blocks to construct the quantum circuit for this operator. Numerical experiments on graphs of different sizes indicate that our algorithm can achieve a high approximation ratio with fewer circuit layers on most instances and exhibit clear performance advantages compared with the QAOA method for this problem.</p>