We have numerically investigated the characteristics of the flow and mixing in a microchannel using magnetic particles. The main flow is driven by the pressure gradient along the channel, while the secondary flow for the mixing is induced by the drag forces of the particles. Here, the particles can move in the flow due to the strong attraction under the periodically-varying magnetic field generated by electromagnets. For the study, the fractional step method based on the finite volume method is used to obtain the velocity field of the fluid and the trajectories of the particles. This study aims at achieving good mixing by periodically changing the direction of magnetic actuation force in time to activate the interaction between the particles and the flow. The quality of mixing is estimated by considering the mixing index and $Poincaracute{e}$ section. In this study, parameter studies on the switching frequency, the magnetic actuation force, the number of magnetic particles and so on are performed to understand their effects on the flow and mixing. Results show that the clustering of magnetic particles during the magnetic actuation plays an important part in good mixing. It is also found that the magnetic force magnitude and switching frequency are the two main parameters that make a combined influence on the mixing efficiency. Such a mixing technique using magnetic particles would be an alternative, effective application for the flow and mixing in a microchannel.