The behaviour of the two-dimensional gravity current in an oscillatory flow is investigated by computation when homogeneous fluid and another fluid of slightly different density were released in a sinusoidally oscillating flow. The incompressible Navier-Stokes equation for an inhomogeneous fluid and the transport equation for solute were solved by the finite volume method developed in the previous paper and extended by incorporating the oscillatory ambient flow with the implementation of the unsteady inflow and outflow boundary conditions. The results indicate that since the tail wind pushes the head forward further than the head wind brings it backward, the mean speed of the current front increases in oscillatory ambient flows. The change of the ambient flow direction makes the front distorted remarkably and enforces the instability of the density interface at some KC numbers. This instability causes the roll up of the interface and the vortex shedding from the head, both of which increase the entrainment rate in low Froude numbers. It is found that the unsteady boundary layer along the wall affects the inner structure of the current head according to oscillatory flows.