Grove first entered the Wimbledon men's singles in 1881, when he lost in round one.

In June 1886 he won the prestigious Northern Championships,[4][5] defeating the American player James Dwight in 3 sets and again in 1887.

[6][7] In May 1887 he won the Scottish Championships defeating Patrick Bowes-Lyon in five sets.

In 1888 he reached the final of the Scottish Championships for the second successive year where his opponent was Bowes-Lyon.

[8] He last entered Wimbledon in 1893, when he lost in the opening round.