The First-Order Reliability Method is applied to bridge flutter instability considering uncertainties in structural damping, flutter derivatives and extreme wind velocity. The baseline is to set each flutter derivative value as a random variable for computing the failure probability by flutter. The flutter speed is obtained by solving the dynamic equilibrium equation. Hence performance function cannot be expressed explicitly. Reliability sampling methods are not considered in this paper because it would require a large computational time. A modification of Hasofer-Lind-Rackwitz-Fiessler algorithm is proposed for avoiding numerical oscillations. Finally, the methodology proposed is applied to the Messina bridge project.