A novel passive micromixer with slanted grooves on the top and bottom of curved microchannel, denoted as CMG, is investigated numerically. The total mixing length is fixed at approximate 5.17 mm. The curved channel is applied to generate Dean vortices in the microchannel at high Reynolds numbers. The slanted grooves are used to assist to create the rotation of flow at low Reynolds numbers. The validation of present numerical simulation is done through the comparison with literatures. Three parameters, the slanted angle (), the grooves width angle (), and the height ratio of grooves (Hg/H), are selected to achieve the optimization. The tested Reynolds numbers range from 1 to 50. Compared with slanted grooved micromixer (SGM) and the curved microchannel (CM), the present micromixer has better mixing efficiency. In order to investigate the flow characteristics, a particle located at one inlet is selected and the trajectory is performed to observe the flow rotation. The rotation angle is defined to estimate the rotation strength. The results show that CMG has largest rotation angle than CM and SGM, which indicates a stronger rotation/helical motion generated in the curved channel. The mixing efficiency of present design has 60% at Re = 50 with a pressure drop of 1.8 kPa.