Coastal circulations during the (surface condition of an) idealized cold-air outbreak are numerically investigated with two-dimensional, non-hydrostatic model in which a constant bottom-slope exists. The atmospheric forcing during a cold-air outbreak is incorporated as the surface cooling and the wind stress. When the offshore angle of the wind-stress vector, defined as the angle measured from the alongshore axis, is smaller than 45 degrees, a strong downwelling circulation develops near the coast. A sharp density front, which separates the vertically homogeneous region from the offshore stratified region, is formed near the coast and propagates offshore with time. Onshore side of the density front, small-scale circulation cells which are aligned in the direction perpendicular to the bottom begin to develop as the near-coast homogeneous region broadens. The surface cooling enhances greatly the development of the surface mixed layer by convective motions due to hydrostatic instability. The convective motions reach far below the hydrostatically unstable layer which is attached to the surface. The small-scale circulation cells are appreciably modified by the convetion cell and the density front develops far offshore compared to the case of no surface cooling. As to the effect of the bottom slope, the offshore distance of the density front increases (decreases) as the bottom slope decreases (increases), which results from the fact that the onshore volume-transport (Ekman transport) of the low-density upper seawater remains almost constant when the wind-stress is maintained constant. It is shown that the bottom slope is an essential factor for the formation of both the density front and the alongshore current when the surface cooling is the only forcing.