The mathematical form of many optimization problems in engineering is constrained optimization problems. In this paper, an improved genetic algorithm based on two-direction crossover and grouped mutation is proposed to solve constrained optimization problems. In addition to making full use of the direction information of the parent individual, the two-direction crossover adds an additional search direction and finally searches in the better direction of the two directions, which improves the search efficiency. The grouped mutation divides the population into two groups and uses mutation operators with different properties for each group to give full play to the characteristics of these mutation operators and improve the search efficiency. In experiments on the IEEE CEC 2017 competition on constrained real-parameter optimization and ten real-world constrained optimization problems, the proposed algorithm outperforms other state-of-the-art algorithms. Finally, the proposed algorithm is used to optimize a singlestage cylindrical gear reducer.