Abstract: In this article, we prove two strong laws of large number for negatively associated random variables without stationary distribution. The proof is based on the maximal moment inequality provided by Shao. In this article, we used the conditions about arbitrary a_n ↑ +∞ and 1 ≤p≤ 2, q≥ 1, so we can get many other strong laws of large number for negatively associated random variables without stationary distribution by giving different a_n, p and q, and so the application of the theorems is more extensive.