The permanent magnetic alloy Ce1+εFe4B4(ε= 0.1, B-rich phase) is studied by means of electron diffraction and high resolution electron microscopy. It has been determined that the Ce1+εFe4B4 alloy has a one-dimensional incommensurate modulated structure of Chimney-Ladder type consisting of two overlapped substructures fomed by Ce atoms and Fe-B clusters respectively. The unit cell parameters of Ce substructure are a = 7.08?, cCe= 3.51-3.60?, and the possible space groups are I4,I4,I4mm, I4/m, I4/mmm. The unit cell parameters of Fe-B substructure are a = 7.08?, cFe= 3.91?, and the space group is P/42/mcm. All of the major and satellite diffraction spots are indexed by using of four indexes method. The high resolution electron microscopic image shows contrast modulation bands corresponding to the modulated structure. The fluctuation of the period of Ce substructure has been observed and discussed. The orientational anormaly caused by the possible deviation of Ce atomic planes from the (a, b) plane is also discused.