A new type of tunable gradient-index (GRIN) microfluidic lens is proposed, which is based on the convection-diffusion process. By using the finite element method, the spatial distribution of the refractive-index (RI) determined by the concentration distribution in the microchannel is analyzed. Results show that the distribution of RI in the microchannel can be tuned by different flow rates of the core and cladding liquid streams. Furthermore, although taking into consideration the existence of the viscous resistance between the channel wall and the flowing stream, the RI distribution is still dependent on the combination of flow rates of the core and cladding streams. This microfluidic lens can be applied to dynamic adjustment of focusing, splitting or bending light beams. It therefore may have extensive applications in the optofluidic optical detecting system and microscale imaging system.