High resolution spectra of the A (1)Sigma(+)--> X (1)Sigma(+) system of the KRb molecule, obtained after excitation using a titanium-doped sapphire laser, were recorded on a Connes-type Fourier transform interferometer. Molecular constants of the first 88 vibrational levels of the X (1)Sigma(+) state are determined, and the potential energy curve is derived up to an internuclear distance of 10.419 Angstrom (99.3% of the potential well depth). The energy of the dissociation limit is found as D-e=4217.3 (15) cm(-1) (referred to the bottom of the potential curve well), in good agreement with the theoretical predictions of Jenc and Brandt [J. Mol. Spectrosc. 154, 226 (1992)] who gave D-e=4220 (20) cm(-1) and the value D-e=4217.4 (8) cm(-1) reported by Kasahara [J. Chem. Phys. 111, 8857 (1999)]. (C) 2000 American Institute of Physics. [S0021-9606(00)01015-1].