In last few years, femtosecond laser pulses with GHz burst mode, which contains ultrashort laser pulse (intra-pulses) trains with a pulse interval of several hundred ps, shows some distinct features in material processing.  In this study, we apply the GHz burst mode femtosecond laser pulses to formation of laser-induced periodic surface structures (LIPSS) in order to explore the new capability of  GHz burst mode processing.  In the experiment, linearly polarized femtosecond laser pulses (wavelength: 1030 nm, pulse width: 220 fs) were focused onto the surface of single crystalline silicon (100) substrate. As a result, one-dimensional (1D) LIPSS were fabricated by conventional femtosecond laser pulses (single mode)  in the whole area inside the laser spot. The period of LIPSS is measured to be approximately 796 nm and its direction is perpendicular to the laser polarization direction. In contrast, in the case of GHz burst mode femtosecond laser pulses created novel 2D LIPSS, in which both the periodic structures perpendicular and parallel to the polarization direction were generated. The period of LIPSS perpendicular and parallel to the polarization direction were measured to be approximately 617 nm and 1240 nm, respectively. We attribute the formation mechanism of 2D LIPSS to generation of hot spots with highly enhanced electric fields in the nanogrooves of LIPSS by the latter part of intra-pulses.