Femtosecond laser pulses with GHz burst mode that consist of a series of trains of ultrashort laser pulses with a pulse interval of several hundred picoseconds offer distinct features in material processing that cannot be obtained by the conventional irradiation scheme of femtosecond laser pulses (single-pulse mode). However, most studies using the GHz burst mode femtosecond laser pulses focus on ablation of materials to achieve high-efficiency and high-quality material removal. In this study, we explore the ability of the GHz burst mode femtosecond laser processing to form laser-induced periodic surface structures (LIPSS) on silicon. It is well known that the direction of LIPSS formed by the single-pulse mode with linearly polarized laser pulses is typically perpendicular to the laser polarization direction. In contrast, we find that the GHz burst mode femtosecond laser (wavelength: 1030 nm, intra-pulse duration: 220 fs, intra-pulse interval time (intra-pulse repetition rate): 205 ps (4.88 GHz), burst pulse repetition rate: 200 kHz) creates unique two-dimensional (2D) LIPSS. We regard the formation mechanism of 2D LIPSS as the synergetic contribution of the electromagnetic mechanism and the hydrodynamic mechanism. Specifically, generation of hot spots with highly enhanced electric fields by the localized surface plasmon resonance of subsequent pulses in the bursts within the nanogrooves of one-dimensional LIPSS formed by the preceding pulses creates 2D LIPSS. Additionally, hydrodynamic instability including convection flow determines the final structure of 2D LIPSS.