The main purpose of this article is to study Fermat-type complex differential-difference equations $f^{(k)}(z{)}^2+[\alpha f(z+c)-\beta f(z){]}^2=R(z)$. Our results improve some results due to Wang–Xu–Tu [AIMS. Mathematics, 2020], Zhang [Bull. Korean. Math. Soc, 2018], and Long–Qin [Applied Mathematics-A Journal of Chinese Universities, 2024]. Moreover, we provide some examples to show the existence of the solutions.