Focusing on the defects, such as slow convergence and premature phenomenon, in solving constrained optimization problems by the traditional Differential Evolution (DE) algorithm, a novel DE based on Simplex-Orthogonal experimental design (SO-DE) algorithm was proposed. The algorithm designed a new hybrid crossover operator that combined simplex crossover and orthogonal experimental design to improve the search ability of DE algorithm, and the improved comparison criteria was used to compare and select the individuals of population. Several parent individuals were used to produce multiple offspring individuals by simplex crossover in the new hybrid crossover operator, then the multiple excellent individuals, which were selected from two set by orthogonal experimental design, were copied in the next generation. Different treatment schemes were used for different stages of population in the improved comparison criterion, which aimed to effectively weigh the relationship between the value of the objective function and the degree of constraint violation, thus better individuals were chosen into the next generation. Simulation experiments were conducted on 13 standard test functions and 2 engineering design problems. The SO-DE algorithm is much better than HEAA (Hybrid Evolutionary Algorithm and Adaptive constraint-handling technique) and COEA/ODE (a novel Constrained Optimization Evolutionary Algorithm based on Orthogonal Experimental Design) in terms of the accuracy and standard variance of final solution. The experimental results demonstrate that the SO-DE algorithm has better accuracy and stability.