  In this paper, we present some basic properties concerning the
quasi-derivation algebra $QDer(\mathcal{A})$ and the quasi-centroid algebra
$QC(\mathcal{A})$ of associative algebra $\mathcal{A}$. Furthermore, using the
result on classification of two, three and four dimensional associative
algebra, we compute, for all two, three and four dimensional associative
algebras, quasi-derivation algebra $QDer(\mathcal{A})$
  and the quasi-centroid algebra $QC(\mathcal{A})$ algebras and give their
corresponding dimension.
