The ultra-wide bandgap semiconductor gallium oxide β-Ga₂O₃ with enhanced resistance to the irradiation and temperature is favorable for high-power and high-temperature optoelectronic devices. β-Ga₂O₃ also exhibits great potential applications in the field of integrated photonics because of its compatibility with the CMOS technique. However, a variety of intrinsic and extrinsic defects and trap states coexist in β-Ga₂O₃, including vacancies, interstitials, and impurity atoms. The defect-related carrier dynamics in β-Ga₂O₃ not only adversely affect the optical and electrical properties, but also directly limit the performance of β-Ga₂O₃ based devices. Therefore, a comprehensive understanding of the carrier transportation and relaxation dynamics induced by intrinsic defects is very important. Supercontinuum-probe spectroscopy can provide a fruitful information about the carrier relaxation processes in different recombination mechanisms, and thus becomes an effective way to study the defect dynamics. In this work, we study the dynamics of carrier trapping and recombination induced by intrinsic defects in pristine β-Ga₂O₃ crystal by using wavelength-tunable ultrafast transient absorption spectroscopy. The broadband absorption spectra induced by the intrinsic defects are strongly dependent on the polarization of pump pulse and probe pulse. Particularly, two absorption peaks induced by the two defect states can be extracted from the transient absorption spectra by subtracting the absorption transients under two probe polarizations. The observed defect-induced absorption features are attributed to the optical transitions from the valence band to the different charge states of the intrinsic defects (such as gallium vacancy). The data are well explained by a proposed carrier capture model based on multi-level energies. Moreover, the hole capture rate is found to be much greater than that of the electron, and the absorption cross-section of the defect state is at least 10 times larger than that of free carrier. Our findings not only clarify the relationship between intrinsic defects and photogenerated carrier dynamics, but also show the importance in the application of β-Ga₂O₃ crystals in ultrafast and broadband photonics.