As for the definition of an ideal I of a commutative ring R which is called a cancellation ideal, this paper establishes an equivalent characterization for cancellation ideals in a (von Neumann) regular arithmetical ring, uses the map φ:Lat(R)→Lat(I):for any A∈Lat(R),φ(A)=I∩A to study the relationship between R and I, then successfully gets the conclusion that 0≠e∈Idem(R), there exists 0≠f∈Idem(I), such that Re=Rf, therefore gives the equivalent condition for cancellation ideal in completely arithmetical ring: R is a completely arithmetical ring and J(R)=0, then I is a cancellation ideal if and only if for any e∈Idem(R), there exists f∈Idem(I), so that Re=Rf.