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Levstein and Maldonado [F. Levstein, C. Maldonado, The Terwilliger algebra ofthe Johnson schemes, Discrete Mathematics 307 (2007) 1621--1635] computed theTerwilliger algebra of the Johnson scheme $J(n,m)$ when $3m\leq n$. In thispaper, 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, andcalculate its dimension.

The Terwilliger algebra of the incidence graphs of Johnson geometry