The ultrafast third-order optical nonlinearity of c-plane GaN crystal, excited by ultrashort (fs) high-repetition-rate laser pulses at 1550 nm, wavelength important for optical communications, is investigated for the first time by optical third-harmonic generation in non-phase-matching conditions. As the thermo-optic effect that can arise in the sample by cumulative thermal effects induced by high-repetition-rate laser pulses cannot be responsible for the third-harmonic generation, the ultrafast nonlinear optical effect of solely electronic origin is the only one involved in this process. The third-order nonlinear optical susceptibility of GaN crystal responsible for the third-harmonic generation process, an important indicative parameter for the potential use of this material in ultrafast photonic functionalities, is determined.