Using the capillary chromatography column as a one-dimensional hydrothermal micro-reactor, we developed a method to produce carbon microfibers with hierarchy structures, in which reduced graphene oxide (rGO) and acid-oxidized single-walled carbon nanotubes (SWCNTs) self-assembled into an interconnected SWCNT network with rGO sheets interposed along the microfiber axis to create a mesoporous microstructure of a large specific surface area (396 m2/g) and a high electrical conductivity (102 S/cm). The resultant carbon hybrid fiber showed ultrahigh specific volumetric capacity of 305 F/cm3 (at 73.5 mA/cm3 by three-electrode cell) in H2SO4 or 300 F/cm3 (at 26.7 mA/cm3 by two-electrode cell) in a polymer gel electrolyte (PVA/H3PO4). The corresponding fiber-shaped all-solid-state flexible micro-supercapacitors with the PVA/H3PO4 electrolyte, but without binder, current collector, or separator, exhibited a long cycle life and an ultrahigh volumetric energy density of ~6.3 mWh/cm3. This value of volumetric energy density is well comparable to a 4V/500-µAh thin-film lithium battery, while the power density of our micro-supercapacitors is more than two orders of magnitude higher than the battery. Furthermore, the all-carbon hybrid fibers can be controllably functionalized to yield versatile fibers with either capacitive or Faradic characteristics for designing high-performance asymmetric fiber micro-supercapacitors. The capacitive-type N-doped rGO/SWCNT fibers obtained through in situ N-doping with urea in the flexible capillary column show tunable specific capacitances from 1.75 to 2.37 mF cm-1, while the Faradic-type fibers created by redox deposition of MnO2 on the rGO/SWCNT fibers have specific capacitances ranging from 1.76 to 3.30 mF cm-1. Both types of functionalized fibers outperform the pristine rGO/SWCNT fibers (1.5 mF cm-1), while retaining fiber geometry and mechanical flexibility. By matching the specific capacitances of one MnO2-coated rGO/SWCNT fiber as battery-type (positive) electrode and the other N-doped rGO/SWCNT fiber as capacitor-type (negative) electrode to achieve the charge balance between two fiber electrodes, we designed and constructed the fiber-based solid-state asymmetric micro-supercapacitors with polymer gelled neutral electrolyte on a flexible polymer substrate. The optimized device exhibits a stable and high voltage window of 1.8 V and excellent cycling stability (87% capacitance retention after 10,000 cycles), as well as good flexibility. These fiber-shaped flexible micro-supercapacitors can be easily integrated into miniaturized power sources for various portable flexible optoelectronics, multifunctional textiles, sensors, and energy devices, as exemplified by powering a TiO2-based UV photodetector and a commercial light-emitting-diode.