<p>This article investigates the effects of G-Brownian motion and impulses on the attractiveness and stability of solutions to neutral functional non-autonomous integro-differential equations. Based on resolvent operators theory and the Banach fixed point theorem, we first study the existence of solutions to the neutral functional non-autonomous integro-differential equations with impulse. Then by Borel–Cantelli lemma and integral inequality, we further investigate attracting and quasi-attracting sets, <i>p</i>-th moment stability and almost sure stability of solutions to the impulsive equation. Moreover, we attempt to study Hyers–Ulam and Ulam–Hyers–Rassias stability of solutions of the neutral functional non-autonomous integro-differential equations without impulse by Grönwall-type inequality. Finally, we exemplify our theoretical results by discussing the heat flow in materials.</p>