A series of carbon-doped single crystals with nominal compositions FeSe0.5Te0.5 were synthesized by self-flux method. X-ray diffraction indicated that the lattice parameter c increases with increasing carbon content, suggesting carbon atoms enter the lattice. The critical current densities were measured and the flux pinning mechanism and its change with doping were analyzed. These samples showed a higher Jc in high magnetic fields as well as a narrower superconducting transition. We have studied the impact of the carbon introduction into FeSe0.5Te0.5 on the temperature dependence of the irreversibility field Hirr(T) and upper critical (Hc2). The pinning mechanism is obtained in the system via the Jc analysis.