A new one-dimensional variational (1D-Var) retrieval method for ionospheric GNSS ra- dio occultation (GNSS-RO) measurements is described. The forward model implicit in the retrieval calculates the bending angles produced by a one-dimensional ionospheric electron density profile, modeled with multiple “Vary-Chap” layers. It is demonstrated that gradient based minimisation techniques can be applied to this retrieval problem. The use of ionospheric bending angles is discussed. This approach circumvents the need for Differential Code Bias (DCB) estimates when using the measurements. This new, general retrieval method is applicable to both standard GNSS-RO retrieval problems, and the truncated geometry of EUMETSAT’s Metop Second Generation (Metop-SG), which will provide GNSS-RO measurements up to about 600 km above the surface. The climatological a priori information used in the 1D-Var is effectively a starting point for the 1D-Var minimisation, rather than a strong constraint on the final solution. In this paper the approach has been tested with 143 COSMIC-1 measurements. We find that the method converges in 135 of the cases, but around 25 of those have high “cost at convergence” values. In the companion paper (Elvidge et al., 2023), a full statistical analysis of the method, using over 10,000 COSMIC-2 measurements, has been made.