He attended St. James Parochial School from 1857 to 1863, De La Salle Institute from 1863 to 1867, and graduated from Manhattan College.
Then he worked in the Corporation Counsel's office, collecting evidence relative to the fraudulent claims of the Tweed era.
During the following presidential campaign, Grady supported Benjamin F. Butler, the candidate of the Greenback and Anti-Monopoly parties.
The Democrats were in the majority in 1911, and Grady expected to be chosen President pro tempore, but was embittered when Tammany boss Charles Francis Murphy selected Robert F. Wagner instead.
He died on February 3, 1912, at his home at 151 East 30th Street, in Manhattan, of diabetes, was buried at the Calvary Cemetery in Queens.