The rapid development of power-intensive and flexible electronic devices requires thinner heat-dissipation devices with better thermal performance. Ultra-thin flat heat pipe (UTFHP) with striped wick structure is a promising candidate for this application, but its wick structure and thermal performance have not yet been thoroughly studied and optimized for the small concentrated heat source, which is commonly encountered in electronics. In this study, several concentrated striped composite wick (CSCW) structures for 0.6 mm thick UTFHPs are proposed and experimentally investigated. The CSCW consists of copper foam with striped passages converging in the heating zone and double layers of copper screen mesh. The thermal performance of UTFHPs with various composite wick structures is experimentally evaluated. UTFHPs with the proposed structures are also compared with a UTFHP with a more conventional parallel passage composite wick structure. Experimental results show that the CSCW with the hollow structure at the evaporation section is preferred, due to the directed liquid working medium reflux and a large vapor-liquid evaporation interface. Besides, the passage width of the copper foam significantly affects the thermal performance. With the best-performing wick structure, the UTFHP gives the lowest thermal resistance of 0.79 °C/W at a heat load of 23.34 W. Its effective thermal conductivity is approximately 7 times that of copper. The proposed striped wick structure for UTFHPs provides an alternative to handle the hot-spot challenge of electronic devices.