Satellite observations of acoustic-gravity waves in the polar regions of the atmosphere indicate a close connection of these waves with wind flows. The paper investigates the peculiarities of the propagation of AGWs in spatially inhomogeneous wind flows, where the flow speed slowly changes in the horizontal direction. A system of hydrodynamic equations was used for the analysis, which takes into account the wind flow with spatial heterogeneity. Unlike the system of equations written for a stationary medium (or a medium moving at a uniform speed), the resulting system contains components that describe the interaction of the waves with the medium. It is shown that the influence of heterogeneous background parameters of the medium can be separated from the effects of inertial forces by means of the special substitution of variables. The analytical expression was obtained that describes the changes in the wave amplitude in a medium moving with a non-uniform speed. This expression contains two functional dependencies: 1) the linear part caused by changes in the background parameters of the medium, which does not depend on the direction of wave propagation relative to the flow; 2) the exponential part associated with the inertia forces, which determines the dependence of the amplitudes of AGWs on the direction of their propagation. The exponential part shows an increase in the amplitudes of the waves in the headwind and a decrease in their amplitudes in the downwind. The obtained theoretical dependence of the amplitudes of AGWs on the wind speed is in good agreement with the data of satellite observations of these waves in the polar thermosphere.