In view of the fact that the simple analytic model is important both in acquiring the dynamic rule of Ocean and in understanding its mechanical essence, a unified solution of transient Ekman drift model encompassing the Fredholm’s solution with constant wind and the hidaka, Nomitsu, and Defant’s solution with unsteady wind is provided, and the paradox that it is uncertain if the solution satisfies the boundary condition is pointed out and explained. The present study shows that a simply mathematical treatment is able to remove this paradox, hoping to call for the mathematicians’ notice. In view of the fact that the simple analytic model is important both in acquiring the dynamic rule of the ocean and in understanding its mechanical essence, a unified solution of transient Ekman drift model encompassing the Fredholm’s solution with constant wind and the hidaka, Nomitsu, and Defant’s the present study shows that a simply mathematical treatment is able to remove this paradox, hoping to call for the mathematicians’ notice.