Corannulene has been a useful prototype for studying C-based nanostructures as well as surface chemistry and reactivity of sp(2)-hybridized carbon-based materials. We have investigated fluorination and hydrogenation of corannulene carrying out density functional theory calculations. In general, the fluorination is energetically more favorable than hydrogenation of corannulene. The substitution of the peripheral H atoms in the corannulene molecule by F atoms leads to a larger cohesive energy gain than when F (or H) atoms are bonded to the hub carbon and bridge carbon sites of this molecule. As expected for doped C-based nanostructures, the hydrogenation or fluorination significantly changes the HOMO-LUMO gap of the system. We have obtained HOMO-LUMO gap variations of 0.13-3.46 eV for F-doped and 0.38-1.52 eV for H-doped systems. These variations strongly depend on the concentration and position of the incorporated F/H atoms, instead of the structural stability of the doped systems. Considering these calculations, we avoid practical difficulties associated with the addition/substitution reactions of larger curved two-dimensional (2D) carbon nanostructures, and we obtain a comprehensive and systematic understanding of a variety of F/H 2D doped systems.