We have calculated quasiparticle current–voltage characteristics J( V) for non-symmetric CDWS–I–N tunnel junctions between a partially gapped charge-density wave (CDW) s-wave superconductor and a normal metal (I stands for an insulator), as well as for symmetric CDWS–I–CDWS junctions. Relevant parameters of CDWS are considered spatially inhomogeneous in accordance with experimental data for various cuprates, especially Bi 2Sr 2CaCu 2O 8+ δ (BSCCO). The calculated dependences G( V) = d J( V)/d V demonstrate conspicuous dip-hump structures (DHSs) at low temperatures, T, and pseudogap shallow well at high T > T c above the critical temperature. In CDWS–I–N junctions, DHSs were shown to be observed for either one or both voltage polarities, depending on the CDW order parameter phase. Similar symmetric DHSs were found for CDWS–I–CDWS junctions. J( V) for break-junctions made of BSCCO were measured. Qualitative agreement was reached between our theoretically calculated and experimental G( V) dependences.