This paper presents a convective time-domain equivalent-source method for determining the scattered acoustic pressure field in a uniform moving medium. The proposed method is based on the solution of the time-domain convective Ffowcs Williams–Hawkings (FW–H) equation while the strengths of equivalent sources are determined by the required pressure gradient boundary condition on the scattering surface. The scattered acoustic pressure can be calculated once the strengths of equivalent sources have been determined. The current paper adopts the recently published analytical time-domain formulation for the acoustic pressure gradient in a moving medium to evaluate the incident pressure gradient on the scattering surface. This makes the proposed method considerably more efficient and accurate than a direct method. The total acoustic pressure consists of the scattered and the incident components. The latter can be obtained by the time-domain acoustic pressure formulation of the convective FW–H equation. Causes of possible instability in the proposed method are analyzed and an effective stabilizing method is proposed. Three test cases are considered to demonstrate the validity of the proposed method: a point monopole source field scattered by: (1) a rigid sphere in a stationary medium, (2) an infinite flat plate in uniform flow parallel to its surface, and (3) a cylinder of infinite length in axial uniform flow. To demonstrate the usefulness of the proposed method in practical engineering applications, the scattering of a point monopole source field by a slender wing in uniform flow is considered.