Glass formation and structural properties of the unconventional lead cuprate glasses of compositions (CuO)x(PbO)100-x (mol %), are reported for the first time. X-ray diffraction and electron microscopic studies show that the glass formation occurs for x = 15-50 mol %. The compositional dependence of the density, molar volume, and glass transition temperature suggests that all glass compositions in this domain have the same topology and network connectivity. The glass structure is built up of [PbO4] tetrahedral units. On heat treatment above glass transition temperatures, the glasses crystallize to CuO and PbO. Electron Spin Resonance (ESR) spectra of the glass compositions consist of broad resonance lines.