This paper characterizes ideal structure of the uniform Roe algebra B* (X) over sinple cores X. A necessary and sufficient condition for a principal ideal of B*(X) to be spatial is given and an example of non-spatial ideal of B* (X) is constructed. By establishing an one-one correspondence between the ideals of B* (X) and the ω-filters on X, the maximal ideals of B* (X) are completely described by the corona of the Stone-Cech compactification of X.