An iterative method to determine the self-consistent orbital solutions of single-lined spectroscopic binaries (SB1s) along with compatible physical properties of component stars via a simultaneous fit including both the Hipparcos Intermediate Astrometric Data (HIAD) and radial velocity data is introduced in this work. For the method, a stellar evolutionary model is used to distribute the total mass and luminosity to the primary and the secondary and update the ratio of the semimajor axes of the photocenter to the primary orbits. Once the Gaia Intermediate Astrometric Data (GIAD) are released, the method can be applied to study the Gaia SB1s and give self-consistent orbital solutions and compatible physical properties of component stars.