Superconductivity in a system with crystal structure modulation (charge density wave - CDW) is described. The modulation is considered to result from electron-hole pairing instability in a quasi-two-dimensional one-band metal with Fermi surface nesting and not 1/2-filling of the band. The density of states square root singularity caused by CDW formation and favouring a dramatic superconducting transition temperature increase is shown to remain in the system under consideration. It is concluded that the inhomogeneous superconductivity is induced by coexistence of the dielectric (CDW) and superconducting ordering. 29 refs.; 1 fig.