  The edge blow-up of a graph $F$ is the graph obtained from replacing each
edge in $F$ by a clique of the same size where the new vertices of the cliques
are all different. In this article, we concern about the Tur\'an problem for
the edge blow-up of trees. Erd\H{o}s et al. (1995) and Chen et al. (2003)
solved the problem for stars. The problem for paths was resolved by Glebov
(2011). Liu (2013) extended the above results to cycles and a special family of
trees with the minimum degree at most two in the smaller color class (paths and
proper subdivisions of stars were included in the family). In this article, we
extend Liu's result to all the trees with the minimum degree at least two in
the smaller color class. Combining with Liu's result, except one particular
case, the Tur\'an problem for the edge blow-up of trees is completely resolved.
Moreover, we determine the maximum number of edges in the family of $\{K_{1,k},
kK_2, 2K_{1,k-1}\}$-free graphs and the extremal graphs, which is an extension
of a result given by Abbott et al. (1972).
