Rotationally resolved spectra of the H3Σu--X3Σg- electronic transition bands of Si2 have been experimentally studied using laser-induced fluorescence in the 380-520 nm range. Si2 molecules are produced in a supersonically expanding planar plasma by discharging a silane/argon gas mixture. In total, 44 bands belonging to the H3Σu--X3Σg- electronic transition system of the most abundant isotopologue 28Si2 are experimentally recorded. With a spectral resolution of ∼0.04 cm-1, the triplet spin-splitting structures in individual rotational transition lines are fully resolved. Detailed analyses on the high-resolution spectra have yielded an accurate determination of spectroscopic constants for both X3Σg- and H3Σu- states. The spin-spin interaction constants for the two triplet states are found to be comparable (λ ≈1.5 cm-1), which may originate from the 3p atomic orbital interaction in the triplet Si2 molecule. The measured isotopologue spectra of 29Si28Si and 30Si28Si indicate that the H3Σu--X3Σg- transition system of 29S28S and 30S28S can be reasonably reproduced by the isotope mass-scaling rule. Spectroscopic parameters, including the Franck-Condon factors, the Einstein coefficients, and the oscillator strengths, are also determined from the experimental results and the Rydberg-Klein-Rees (RKR) calculations. The agreement between the experimentally measured and calculated dispersed fluorescence spectra indicates that the RKR calculations with the molecular constants determined in this work can accurately reproduce the diatomic potentials of both states. These molecular data provide a benchmark in high-level theoretical studies on Si2 and likely other small silicon clusters.