Chaotic mixers with twisted microchannels were designed and simulated numerically in the present study. The phenomenon whereby a simple Eulerian velocity field may generate a chaotic response in the distribution of a Lagrangian marker is termed chaotic advection. Dynamic system theory indicates that chaotic particle motion can occur when a velocity field is either two-dimensional and time-dependent, or three-dimensional. In the present study, micromixers with three-dimensional structures of the twisted microchannel were designed in order to induce chaotic mixing. In addition to the basic T-mixer, three types of micromixers with inclined, oblique and wavelike microchannels were investigated. In the design of each twisted microchannel, the angle of the channels' bottoms alternates in each subsection. When the fluids enter the twisted microchannels, the flow sways around the varying structures within the microchannels. The designs of the twisted microchannels provide a third degree of freedom to the flow field in the microchannel. Therefore, chaotic regimes that lead to chaotic mixing may arise. The numerical results indicate that mixing occurs in the main channel and progressively larger mixing lengths are required as the Peclet number increased. The swaying of the flow in the twisted microchannel causes chaotic advection. Among the four micromixer designs, the micromixer with the inclined channel most improved mixing. Furthermore, using the inclined mixer with six subsections yielded optimum performance, decreasing the mixing length by up to 31% from that of the basic T-mixer.