This paper proposes an improved $\epsilon$ constrained handling method (IEpsilon) for solving constrained single-objective optimization problems (CSOPs). The IEpsilon method adaptively adjusts the value of $\epsilon$ according to the proportion of feasible solutions in the current population, which has an ability to balance the search between feasible regions and infeasible regions during the evolutionary process. The proposed constrained handling method is embedded to the differential evolutionary algorithm LSHADE44 to solve CSOPs. Furthermore, a new mutation operator DE/randr1*/1 is proposed in the LSHADE44-IEpsilon. In this paper, twenty-eight CSOPs given by “Problem Definitions and Evaluation Criteria for the CEC 2017 Competition on Constrained Real-Parameter Optimization” are tested by the LSHADE44-IEpsilon and four other differential evolution algorithms CAL-SHADE, LSHADE44+IDE, LSHADE44 and UDE. The experimental results show that the LSHADE44-IEpsilon outperforms these compared algorithms, which indicates that the IEpsilon is an effective constraint-handling method to solve the CEC2017 benchmarks.