In this paper we introduce the notion of almost idempotent semirings as the semirings with semilattice additive reduct satisfying the identity x + x 2 = x2, and characterize eight subclasses of the variety AI of all almost idempotent semirings corresponding to the eight subvarieties of the variety Nℬ of all normal bands. Every almost idempotent semiring S is a distributive lattice of rectangular almost idempotent semirings. Given a semigroup F, the semiring Pf(F) of all finite non-empty subsets of F is almost idempotent precisely when F is a band, and in this case, P f(F) is freely generated by the band F in the variety AI. This semiring Pf(F) is free in a subclass of A I if and only if F is in the corresponding subvariety of Nℬ. © 2010 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Suzhou University.