The private course was established in 1927 on dunes-laden terrain that required very little earth-moving. The original layout was designed by Mr H.L. (Cargie) Rymill and was used for twenty years, before compulsory land acquisitions for the new Adelaide Airport required the course to be redesigned. Vern Morcom of Kingston Heath was engaged as the architect for the reorientated course in 1947.

In 1998, architects Neil Crafter and Bob Tuohy restored the design to its original links characteristics, converting greens to Bent grass, and conserving and re-establishing native indigenous plants, grasses and trees.

Glenelg has hosted many State and national championships throughout its history, including the Australian Amateur Championships (Men and Women), Men's Interstate Series, Australian Junior Championships (Boys and Girls) and South Australian Opens and PGAs.

The club has reciprocal privileges with a number of other clubs across Australia. Otherwise, visitors must be either introduced by the general manager (at A$150) or by a club member (at A$55). Visitor play is not permitted on Saturdays.