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The degree constrained minimum spanning tree is a classical NP hard problem in combinatorial optimization, which is widely used in network design and optimization. The existing solution methods can't take the efficiency and precision into account. In order to shorten the solution time and get the optimal solution better, an improved algorithm combining simulated annealing algorithm and single parent genetic algorithm is proposed. Firstly, the generation of mutation factor in genetic algorithm is improved to avoid the generation of infeasible solution individuals, and the adaptive mutation rate is designed to improve the efficiency of the algorithm. Secondly, to solve the problem that only mutation operation of single parent genetic algorithm may lead to individual jump of the optimal solution, combined with the idea of simulated annealing, to ensure the global optimization of the solution. Finally, three groups of experiments are carried out in the specific degree constrained minimum spanning tree problem, which are compared with the traditional single parent genetic algorithm in terms of running time and optimal solution. The experiment shows that the algorithm has better improvement effect in solving efficiency and obtaining optimal solution.