A steering damper device for a two-wheeled vehicle presents a problem with regard to facilitating the viewability of a meter and to increase the degree of freedom of the meter in layout to bring down the center of gravity of the vehicle. A two-wheeled vehicle includes, at a front end of a main frame, a head pipe for rotatively supporting a steering shaft. At the front part of the head pipe, there is installed a meter stay for supporting a meter. Between the head pipe side and the steering shaft side there is interposed a steering damper device for restricting abrupt run-out of the handlebar. The steering damper device is arranged forward of the head pipe and below the meter stay to make effective use of the space of the vehicle and further to increase the degree of freedom of the meter in design.