A graph G is a 2-tree if G=K₃, or G has a vertex v of degree 2, whose neighbors are adjacent, and G-v is a 2-tree. Clearly, if G is a 2-tree on n vertices, then |E(G)|=2n-3. A non-increasing sequence π=(d₁,…,d_n) of nonnegative integers is a graphic sequence if it is realizable by a simple graph G on n vertices. Yin and Li (Acta Mathematica Sinica, English Series, 25(2009)795 13;802) proved that if k≥2, n≥ 9 / 2k²+19 / 2k and π=(d₁,…,d_n) is a graphic sequence with ∑_i=1ⁿ d_i>(k-2)n, then π has a realization containing every tree on k vertices as a subgraph. Moreover, the lower bound (k-2)n is the best possible. This is a variation of a conjecture due to Erdős and Sós. In this paper, we investigate an analogue extremal problem for 2-trees and prove that if k≥3, n≥2k²-k and π=(d₁,…,d_n) is a graphic sequence with ∑_i=1ⁿ d_i> 4kn / 3 -5n / 3, then π has a realization containing every 2-tree on k vertices as a subgraph. We also show that the lower bound 4kn / 3 -5n / 3 is almost the best possible.