The nu(1), nu(2), and nu(3) bands of H2F+ were observed with a Fourier transform absorption spectroscopic technique in the 3 and 7 mu m regions. The ion was produced with a hollow cathode discharge in a F-2, He, and H-2 gas mixture. A simultaneous analysis of FT data combined with laser spectroscopic data was carried out using the Watson's A-reduced Hamiltonian to determine molecular constants in vibrationally excited states. The effect of the vibration-rotation interaction between the nu(1) and nu(3) states was found to be small compared with the case of H2O. The vibration-rotation transitions of the nu(2) band were first identified and analyzed to obtain molecular constants in the nu(2) state, and the band origin was determined to be 1370.5236 (7) cm(-1) with one standard deviation in parentheses. Determined molecular constants can be used to derive the r(e) structure of H2F+ as r(e)(H-F) = 0.9608(6) angstrom, angle(e)(H-F-H) = 112.2(2)degrees with the error corresponding to the uncertainty of the assumed vibration rotation constant gamma(a)(2) and the range of the values derived from three pairs of rotational constants.