Liquid mixing in periodically curved microchannels with strong curvature is studied mainly using a random-walk particle-tracking method. The method uses a large number of particles to simulate fluid mixing. These particles are advected according to the velocity obtained by a grid-based method and undergo a random-walk to simulate the diffusion. For comparison purpose, the convective?diffusive equation for concentration is also solved by a grid-based method and a particle-tracking simulation with an approximate diffusion model (ADM). The present results show that the concentration distributions obtained by the random-walk particle-tracking method and the particle-tracking simulation with an ADM are in good agreement with each other. The details of concentration distribution at the exit of micromixers with strong curvature at higher Peclet numbers can be obtained by the present method. Multi-directional vortices due to large flow rate and strong curvature stretch and distort the interface between different species, and so improve fluid mixing effectively. The results reveal that the influence of channel curvature on fluid mixing increases with the increase of Reynolds number and higher mixing performance appears in the case with stronger curvature at higher Reynolds numbers.