Rangers played a total of 19 competitive matches during the 1894–95 season.
They finished third in the Scottish League Division One, behind Celtic and winners Heart of Midlothian, with a record of 10 wins from 18 matches.
The club ended the season without the Scottish Cup.
They were knocked out of the first round by Heart of Midlothian, losing 2–1 at home.
All results are written with Rangers' score first.