The solar spectrophotometer "Mark-I", located at the Observatorio del Teide and continuously operated for the latest 36, provides a high precision measurement of the radial velocity of the Sun-as-a-star which has enabled the study of the small velocity fluctuations produced by normal modes solar oscillations and the characterization of its spectrum. Furthermore, because of its high sensitivity and long term instrumental stability also provides a daily accurate determination (less than 1 m s^{-1}) of the daily radial velocity offset, the so-called "solar gravitational red-shift" (GRS). In the present work, first results of the analysis of this parameter over the whole period 1976-2011 are presented.