Compounds with incommensurate structural modulations have been extensively studied in last several decades. However, the relationship between structurally incommensurate/commensurate phases and associated electronic states remains enigmatic. Here we report the coexisting of complex incommensurate structures and highly unusual electronic roughness on the surface of in situ cleaved IrTe₂ by using scanning tunnelling microscopy/spectroscopy, corroborated with extensive density-functional theory calculations. This behaviour is traced to structural instability, which induces a structural transition from a trigonal to a triclinic lattice below transition temperature, giving rise to the formation of unidirectional structural modulations with distinct wavelengths, accompanied by the opening of a 'pseudo'-gap in the surface layer. With further cooling the surface adopts a structure that reflects an ~6 × periodicity that is different from the bulk 5 × periodicity. Calculations show that the structure distortion is not associated with a charge density wave, but is rather associated with Te p-electron bonding.