We have investigated the KRb 480 nm system by mass-resolved resonance enhanced two-photon ionization in a cold molecular beam. The 1 (3)Delta(1), 4 (1)Sigma(+), and 5 (1)Sigma(+) <-- X (1)Sigma(+) transitions have been identified. For the 1 (3)Delta(1) and 5 (1)Sigma(+) states, the electronic term values and vibrational constants are determined experimentally for the first time. Potential energy curves of the 4 (1)Sigma(+) and 5 (1)Sigma(+) states undergo multiple avoided crossings with nearby (1)Sigma(+) states in the observed spectral region. For the 4 (1)Sigma(+) state, a vibrational numbering of the experimentally observed levels is suggested. Anomalies in vibronic structures of the 4 (1)Sigma(+) and 5 (1)Sigma(+) states are understood by comparison with high-level ab initio calculations currently available. The avoided crossing energies are also experimentally estimated.