Designing an efficient optimization method which also has a sim- ple structure is generally required by users for its applications to a wide range of practical problems. In this research, an enhanced differential evolution algorithm with adaptation of switching crossover strategy (DEASC) is proposed as a general- purpose population-based optimization method for continuous optimization problems. DEASC extends the solving ability of a basic differential evolution algorithm (DE) whose performance significantly depends on user selection of the control parameters: scaling factor, crossover rate and population size. Like the original DE, the proposed method is aimed at efficiency, simplicity and robustness. The appropriate population size is selected to work in accordance with good choices of the scaling factors. Then, the switching crossover strategy of using low or high crossover rates are incorporated and adapted to suit the problem being solved. In this manner, the adaptation strategy is just a convenient add-on mechanism. To verify the performance of DEASC, it is tested on several benchmark problems of various types and difficulties, and compared with some well-known methods in the literature. It is also applied to solve some prac- tical systems of nonlinear equations. Despite its much simpler algorithmic structure, the experimental results show that DEASC greatly enhances the basic DE. It is able to solve all the test problems with fast convergence speed and overall outperforms the compared methods which have more complicated structures. In addition, DEASC also shows promising results on high dimensional test functions.