With considering the boundary slip at the solid-liquid interface, the heat and mass transfer performances of fluid flow in microchannel heat sinks with three different cross-sectional shapes, i.e., rectangular, elliptical and triangular were studied. The results show that the hydraulic resistance decreases but the convective heat transfer coefficient increases with the increasing of slip length. Under the constraints of fixed slip length and with the same cross-sectional shape, the hydraulic resistance and convective heat transfer coefficient of microchannel heat sinks with any cross-sectional shape decrease with the increase of hydraulic diameter of the microchannel. Regarding the microchannels with three different cross-sectional shapes, it is found that the triangular shaped microchannel has the worst heat transfer performance under the constraint of same cross-sectional area. For the elliptical and rectangular microchannels, the rectangular microchannel has better heat transfer performance when the hydraulic diameter of the microchannel is smaller than a critical value, but the elliptical microchannel has better convective heat transfer performance when the hydraulic diameter of the microchannel is larger than the critical value.