C²-Ray calculates spherical symmetric time-dependent photo-ionization in 1D with the source at the origin for hydrogen only. The code is explicitly photon-conserving and uses an analytical relaxation solution for the ionization rate equations for each time step, thus enabling integration of the equation of transfer along a ray with fewer cells and time steps than previous methods. It is suitable for coupling radiative transfer to gas and N-body dynamics methods on fixed or adaptive grids. C²-Ray is not parallelized but contains an MPI module for compatibility with the 3D version (C²-Ray3Dm).