Transparent conducting oxides (TCOs) exhibit interesting linear and nonlinear optical properties in their epsilon-near-zero (ENZ) region. Studies so far have mostly focused on exploring the optical response of a limited number of these materials. It is therefore important to investigate new TCOs that could offer improved ENZ properties. This work reports for the first time measurements of the linear and nonlinear optical responses of polycrystalline indium-zirconium oxide (IZrO) in the ENZ spectral region. The fabricated IZrO films exhibit high optical mobility (>60 cm2 V-1 s-1) and a broadening of the ENZ region due to a graded permittivity along the thickness, as suggested by spectroscopic ellipsometry. This in turn leads to a broadband nonlinear response with a full-width-at-half-maximum bandwidth as large as ≈260 nm, covering the entire spectral range of the C, L, and U optical telecommunication bands. This work introduces IZrO as a new, promising TCO that could be used for ultrafast and broadband modulation of light in the telecommunication region of the spectrum.