In the present study, thermal performance of a microchannel heat sink with superhydrophobic walls is studied for different ratios of the wall convergence. To this end, three-dimensional Navier-Stokes equations and energy equation subject to the slip boundary conditions, viz. velocity slip and temperature jump, are numerically solved using the finite volume method. Then, the variations of thermal resistance of the heat sink with the number of channels, width- and height-tapered ratios, are studied for a fixed pumping power. The results show that by utilizing the superhydrophobic walls, the optimum width-tapered ratio of the channel is higher than that of the hydrophilic walls. The accentuated effect of the number of channels on thermal performance in the presence of liquid-solid interfacial slip weakens the effect of converging the width of the channel. It is also revealed that the optimum number of channels also increases to give prominence to the effect of interfacial slip by diminishing the smallest dimension of the channel. Finally, it is shown that for a pumping power of 0.05 W, using a heat sink with converging microchannels and superhydrophobic walls, reduces the overall thermal resistance by 28 percent, compared to that with conventional microchannels. In fact, the increase in fluid flow rate resulting from the use of converging microchannels with superhydrophobic walls outweighs the undesirable effect of temperature jump on heat transfer, in a sense that the heat sink performance augments considerably.