Steel–concrete composite bridge decks may risk galloping instability during their bridge-launching phase, since the normally first launched steel boxes could feature bluff and lightweight cross section. In our previous study, a bridge deck of open cross section (typically used in steel–concrete composite bridges) has been found in smooth flow highly prone to the unsteady galloping instability occurring at relatively low reduced wind speed. Considering the natural wind field is usually turbulent, motivations arise to understand what role can the incident turbulence play in the galloping instability of this open cross section deck. New wind tunnel tests were therefore carried out in grid-generated turbulent flow, characterized by an integral length scale comparable to the bridge deck height and an intensity of 9% to 15%. For the interested wind angles of attack around null, static tests first indicate the incident turbulence is able to promote an even higher galloping factor than that in smooth flow, while the Strouhal number shows a decrease. This suggests a higher proneness for the galloping and vortex induced vibration to interact. In aeroelastic tests, however, the typical unsteady galloping instability due to the interaction with vortex induced vibration has never been observed. Instead, the unsteady galloping is initiated in a more complicated manner: unrestricted oscillation arises at a reduced wind speed clearly higher than the Kármán-vortex resonance one even for a very low Scruton number (the mass-damping parameter), combined with the absence of any Kármán-vortex excitation. Nevertheless, similar to the smooth flow condition, the nosed-up 4° remains to be the most unfavorable wind angle of attack in turbulent flow, featuring the lowest galloping onset in the low Scruton number condition. Finally, dependent on the magnitude of Scruton number, it is able to conclude that the incident turbulence can either suppress or promote the galloping instability of this bridge deck.