In this article, we theoretically demonstrate the characteristics of Rayleigh surface wave propagation in a homogeneous and orthotropic thermoelastic half-space in the context of three-phase-lag model of generalized thermoelasticity. The influence of magnetic field on Rayleigh wave is analyzed in the framework of two-temperature model. A vector matrix differential equation is formed by employing normal mode analysis, which is then solved by the eigen function expansion method. The frequency equations in closed form are de- rived and the path of surface particles during Rayleigh wave propagation is found to be elliptical. The results show appreciable differences in phase velocity, attenuation coeffi- cient and specific loss due to the presence of heat-flux phase-lag and is more dominating in comparison with other phase lags.