A femtosecond mode-locked laser is used for what is believed to be the first time as a broadband infrared source for high-resolution Fourier transform absorption spectroscopy. A demonstration is made with a ${\mathrm{Cr}}^{4+}:\mathrm{YAG}$ laser. The entire ${\nu }_1+{\nu }_3$ vibration–rotation band region of acetylene, observed after passing through a single-pass $80\text{-}\mathrm{cm}$ -long cell, is simultaneously recorded between 1480 and $1600\mathrm{nm}$ , in $7.9\mathrm{s}$ with a signal-to-noise ratio equal to 1000. Two hot bands of the most abundant acetylene isotopologue and the ${\nu }_1+{\nu }_3$ band of the ${}^{13}\mathrm{C}^{12}\mathrm{C}{\mathrm{H}}_2$ are also present. Replacement of the usual conventional tungsten lamp by the bright laser source reduces by about a factor of 150 the recording time needed to get similar results. The noise equivalent absorption coefficient at $1\mathrm{s}$ averaging is equal to $7\times {10}^{-7}{\mathrm{cm}}^{-1}{\mathrm{Hz}}^{-1∕2}$ per spectral element.