Given $ n, m\in\mathbb {N} $ with $ m< n $ and Let $ I=\{1,..., n\} $. The Johnson graph $ J (n, m) $ is defined as the graph whose vertex set is $ V=\{v\mid v\subseteq I,| v|= m\} $ and two vertices $ v $, $ w $ are adjacent if and only if $| v\cap w|= m-1$. Let $ n= 2m $. The enhanced Johnson graph $ EJ (2m, m) $ is the graph whose vertex set is the vertex set of $ J (2m, m) $ and the edge set is $ E_2= E\cup E_1 $ where $ E $ is the edge set of $ J (2m, m) $ and $ E_1=\{\{v, v^ c\}| v\subseteq I,| v|= m\} $ and $ v^ c $ is the complement of the subset $ v $ in the set $ I $. In this paper, we show that the diameter of $ EJ (2m, m) $ is $\lceil\frac {m}{2}\rceil $(whereas the diameter of $ J (2m, m) $ is $ m $). Also, we determine the automorphism group of $ EJ (2m, m) $ and we show that $ EJ (2m, m) $ is an integral graph, namely, every its eigenvalue is an integer. Although, some of our results are special cases of Jonse [7], unlike his proof that used some deep group-theoretical facts, ours usesno heavy group-theoretic facts.