Sulfur hexafluoride (SF₆) is a greenhouse gas of very long lifetime. Its infrared absorption spectrum is very important in modeling the atmospheric radiation balances. The SF₆ is also a prototypical system for studying the principles and techniques of laser isotope separation using powerful infrared lasers. As a very heavy molecule, the infrared spectrum of SF₆ at room temperature is very dense, which poses a great challenge to monitoring the relative abundances of different SF₆ isotopomers by direct absorption spectroscopy. Supersonic jet expansions have been widely used to simplify the gas phase molecular spectra. In this work, astigmatic multi-pass absorption cell and distributed feed-back quantum cascade lasers (QCLs) are used to measure jet-cooled rovibrational absorption spectra of ³²SF₆ and ³³SF₆ at 10.6 μm. The spectrometer works in a segmented rapid-scan mode. The gas mixtures (SF₆∶Ar∶He = 0.12∶1∶100) are expanded through an 80 mm \times 300 μm pulsed slit nozzle. Two QCLs running at room temperature are used and each one covers a spectral range of about 3.0 cm^–1. The v₃ fundamental bands of both ³²SF₆ and ³³SF₆ are observed. The rotational temperature of ³²SF₆ and ³³SF₆ in the ground state in the supersonic jet are both estimated at 10 K and the linewidth is about 0.0008 cm^–1 by comparing the simulated spectrum with the observed spectrum with the PGOPHER program. A new weak vibrational band centered around 941.0 cm^–1 is observed and tentatively assigned to the (v₁+v₂+v₃)–(v₁+v₂) hot band of ³²SF₆. The effective Hamiltonian used to analyze the rovibrational spectrum of SF₆ is briefly introduced. A simplified rotational analysis for this hot band is performed with the XTDS program developed by the Dijon group. The band-origin of this hot band is determined to be 941.1785(21) cm^–1. The rotational temperature of this hot band is estimated at 50 K. A new scheme by measuring the jet-cooled absorption spectrum of this hot band of ³²SF₆ and the v₃ fundamental band of ³³SF₆ is proposed for measuring the relative abundance of ³³SF₆/³²SF₆.