  A hom-Lie algebroid is a vector bundle together with a Lie algebroid like
structure which is twisted by a homomorphism. In this paper we use the idea of
representations up to homotopy of Lie algebroids to construct a same structure
for hom-Lie algebroids and we will explain how representations up to homotopy
of length 1 are related to extensions of hom-Lie algebroids.
