Galloping instability relating to cross-wind vibrations can be found in flexible and lightly damped structures. In the present paper, the reliability of a thin-walled steel beam in maintaining its galloping stability was examined using a probabilistic approach. The analysis considered random variation in the cross-sectional geometrical properties of the beam, the material elastic modulus, the structural damping and the wind speed. A large number of Monte Carlo simulations were performed with normal and Gumbel distributions applied to the random variables to determine the probability distribution function of the safety margin. The limit state is considered violated when the wind speed exceeds the onset wind velocity of galloping, resulting in the aerodynamic damping being greater than the structural damping. It was shown by a conventional codified safety factor method that the beam was robust enough for galloping stability. By contrast, the probability-based assessment revealed that the beam failed to achieve the target reliability index in case the coefficient of variation of wind speed was greater than 5%. The analysis results suggested that the code-satisfied slenderness of the beam should be reduced by a factor of 1.5-1.7 under the action of wind speed with a coefficient of variation in the range 30-40%.