Optimizing the groove size of flat micro heat pipes is crucial for improving their thermal performance. In this study, we developed a grooved converging microchannel array for use in a flat micro heat pipe to enhance the capillary force. A simplified theoretical analysis was used to optimize the groove size for given operating conditions of converging microchannels and straight microchannels. The evaporation section of the grooved microchannel was hydrophilic and had a smaller hydraulic diameter than the hydrophobic condensation section. The smaller diameter of the evaporation section enabled the condensed working fluid to be effectively drawn back to the same section. Experiments were performed to measure the thermal performance of the micro heat pipes under the analyzed operating conditions. Compared to a heat pipe with a straight microchannel, and a heat pipe with an unoptimized converging microchannel, the micro heat pipe with the optimized converging microchannel was confirmed to yield a higher thermal performance. Capillary-driven flow experiments at room temperature and atmospheric pressure were also used to investigate the capillary forces of the different microchannels. The optimized converging microchannel was once again observed to generate the largest capillary force.