The 3 (3)Sigma(+)-X (1)Sigma(+) transition of KRb is observed by resonance enhanced two-photon ionization in a pulsed molecular beam. Hyperfine splittings of (KRb)-K-39-Rb-85 and (KRb)-K-39-Rb-87 isotopomers are observed. From the magnitude of hyperfine splittings, we found that the main hyperfine structure was dominated by the Fermi contact interaction between the Rb nuclear spin and the unpaired electron spin. The Fermi contact interaction constants were determined to be 291 MHz for (KRb)-K-39-Rb-85 and 665 MHz for (KRb)-K-39-Rb-87. In the KRb 3 (3)Sigma(+) state the electron spin couples more strongly with the Rb nuclear spin than with other angular momenta, and the energy level structure is well described by the hyperfine angular momentum coupling scheme of the b(betaS) case. The molecular constants and the Rydberg-Klein-Rees potential energy curve of the 3 (3)Sigma(+) state were determined. (C) 2004 American Institute of Physics.