A novel passive micromixer, called a trapezoidal-zigzag micromixer (TZM), is reported. A TZM is composed of trapezoidal channels in a zigzag and split–recombine arrangement that enables multiple mixing mechanisms, including splitting–recombining, twisting, transversal flows, vortices, and chaotic advection. The effects of geometric parameters of the TZM on mixing performance are systematically investigated by the Taguchi method and numerical simulations in COMSOL Multiphysics. The number of mixing units, the slope angle of the trapezoidal channel, the height of the constriction element, and the width ratio between the middle-trapezoidal channel and the side-trapezoidal channel are the four parameters under study. The mixing performance of the TZM is investigated at three different Reynolds number (Re) values of 0.5, 5, and 50. The results showed that a TZM with six mixing units, a trapezoidal slope angle of 75°, a constricting height of 100 µm, and a width ratio of 0.5 has the highest mixing efficiency. This optimal TZM has a mixing efficiency greater than 85% for Re values from 0.1 to 80. In particular, for Re ≤ 0.9 and Re ≥ 20, the mixing efficiency of the optimal TZM is greater than 90%. The proposed TZM has a higher mixing efficiency and a smaller footprint than previously reported micromixers.