This paper presents an analytic time-domain formulation for acoustic pressure gradient prediction in a moving medium, which has significant application potential in evaluating the acoustic scattering boundary condition. Based on the convective Ffowcs Williams – Hawkings equation, a semianalytic time-domain acoustic pressure gradient formulation with a form involving the observer time differentiation outside the integrals is first developed, and then the desired analytic time-domain acoustic pressure gradient formulation is derived. Because the derived formulations are performed directly in the time domain, they are particularly applicable to the moving observer case. Simulation results for a stationary monopole source, a stationary dipole source, as well as a rotating monopole source in a moving medium demonstrate the effectiveness and accuracy of the proposed formulations for both stationary and moving sources with moving observers.