In this talk, we introduce the notion of Atiyah class of a generalized holomorphic vector bundle, which captures the obstruction to the existence of generalized holomorphic connections on the bundle. As in the classical holomorphic case, this Atiyah class can be defined in three different ways: using Cech cohomology, using the first-jet short exact sequence, or adopting the Lie pair point of view. This is a joint work with X. Jia and H. Lang.