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Restuccia and Rinaldo proved that a standard graded $K$-algebra $K[x_1, ...x_n]/I$ is strongly Koszul if the reduced Gr\"obner basis of $I$ with respectto any reverse lexicographic order is quadratic. In this paper, we give asufficient condition for a toric ring $K[A]$ to be strongly Koszul in terms ofthe reverse lexicographic Gr\"obner bases of its toric ideal $I_A$. This is apartial extension of a result given by Restuccia and Rinaldo.  In addition, we show that any strongly Koszul toric ring generated bysquarefree monomials is compressed. Using this fact, we show that oursufficient condition for $K[A]$ to be strongly Koszul is both necessary andsufficient when $K[A]$ is generated by squarefree monomials.

Reverse lexicographic Gr\"obner bases and strongly Koszul toric rings