In this paper, a β channel linear two-layer barotropic quasi-equilibrium ocean model forced by time-varying wind, that is wind anomalies, is established, and its analytical solutions are obtained. It should be noted that the following discussions pertain to the baroclinic mode because the barotropic mode is inconsistent with actual ocean conditions. In the western boundary, the upper corresponding flow field to time-varying wind is expressed as a couple of vortices with cyclonic and anti-cyclonic curvatures. In the upper ocean, obvious western and eastern flow can be forced on the β channel centerline at t=0 and t=T/2, where T is the varying period of wind field, because west and east wind are strongest at that time. Moreover, an obvious countercurrent appears at the south-north lateral boundary of the β channel. Although the forcing of wind disappears near t=T/4 and t=3T/4, oceanic flow anomalies remain due to inertia. In addition, the abnormal flow is strong and changes slowly at t=0 and t=T/2 but becomes weak, acute, and reverses its direction at t=T/4 and t = 3T/4. The corresponding ocean mode also shows that the strength of the lower flow is similar to that of the upper flow; however, the flow is in an opposite direction, which denotes the baroclinicity of the ocean. In analytical solutions, the fluctuation frequency of the ocean flow is the same as its forcing wind field with the exception of a fixed phase difference. Although the nature of the flow anomalies is a quasi-equilibrium vortex wave because only the vortex wave is included in the model, it will transform to a Rossby wave when the forcing wind stress and Rayleigh friction is small. Estimation of the flow amplitude shows that the corresponding flow anomalies become stronger with a higher wind stress, a wider half-width of β channel, a smaller dissipation and a slower changing frequency of wind stress. In addition, the low-frequency wind stress can initiate stronger flow anomalies than those for high-frequency wind stress under the same conditions. The spatial pattern of the corresponding ocean mode is similar to that of the flow anomalies over southeast Honshu Island in Japan. The analytical solutions obtained in this paper can reflect the upper flow anomalies forced by actual wind in the mid-latitude North Pacific to some extent; therefore, these results are helpful for demonstrating the corresponding mechanism of the upper flow to time-varying wind fields.