The present paper is concerned with the study of $\Aut(B(n))$ the automorphism group of a non-associative Boolean rings $B(n)$, where $\left$ is a free 2-group on n generators $\{x_i\}$ $i=1,\dots,n$, subject with $X_i\circ X_j=X_i+X_j$ for $i\neq j$. It is shown that for $n$ even, Aut$(B(n))=S_{n+1}$ and for $n$ odd, Aut$(B(n))=S_n$. An example of a non-associative Boolean ring $R$ of order 8 is provided which shows that in general Aut$(R)$ is not a symmetric group.