We investigated the dynamics of single DNA molecules driven by the electrophoretic force in several tapered contraction-expansion microchannels. Under high localized electric-field gradients, fast transition between the stretching and compression of DNA molecules was achieved. Numerically, a combination of the finite element method and the coarse-grained Brownian dynamics simulation was used to capture the dynamics of single DNA molecules simplified as freely-draining bead-spring wormlike chains. A generalized predictor-corrector time marching scheme was proposed in this work. It was found that the initial conformation, the initial center-of-mass location, and the electric-field strength are three major factors affecting the DNA dynamics. The forced relaxation due to the reverse compression in the expansion zone can speed the relaxation of DNA molecules compared with the free relaxation in the bulk. We have also simulated DNA dynamics in different contraction-expansion microchannels by changing the length or the small-end width of the contraction zone (with other geometrical lengths fixed). Decreasing the small-end width can provide higher DNA stretching due to both increased Deborah number and increased accumulated strain. Increasing the length of the contraction zone, on the other hand, only slightly increases the accumulated strain, while greatly decreases the Deborah number, causing a decrease in DNA stretching. Experimentally, DNA molecules were gradually stretched in the contraction zone and then were quickly compressed back within a short distance outside the contraction zone. DNA chains in different initial configurations demonstrate different behaviors in contraction-expansion microchannels. The Brownian dynamics simulation results are in qualitative agreement with the experimental observations.