  Levstein and Maldonado [F. Levstein, C. Maldonado, The Terwilliger algebra of
the Johnson schemes, Discrete Mathematics 307 (2007) 1621--1635] computed the
Terwilliger algebra of the Johnson scheme $J(n,m)$ when $3m\leq n$. In this
paper, we determine the Terwilliger algebra of the incidence graph $J(n,m,m+1)$
of Johnson geometry when $3m\leq n$, give two bases of this algebra, and
calculate its dimension.
