We have investigated the electronic structure of KxC60 (x = 0-6) using low-energy electron energy loss spectroscopy (LEELS), especially focusing on the K-3p core-electron excitation spectra. It is found that the structure of the K-3p-excitation spectrum of KxC60 quite differs from that of KCI. Furthermore, the K-3p-excitation LEELS of K3C60 has been revealed to be different from that of K6C60. K-3p electrons are excited into K-4s- and K-3d-derived empty states in both KxC60 and KCI, but in the case of KxC60 the K-3d-derived empty states have a rather complicated structure where several levels are not well separated. Consequently, K-3p-excitation LEEL spectra of KxC60 show wide-spread plateau-like structures. The difference in the K-3p- excitation spectra of K3C60 and K6C60 is considered to originate from the different crystal field around K+ cations in the C-60 molecular crystal.