It looks like a cadet uniform from around the turn of the century. I can't make out the initials on the collar but they likely reflect the school he was at. This page has an example of the LSU version, as does this one. The uniform in the picture looks too dark to be LSU and there are only two letters I can make out on the collar.

Because of the Morrill Land Grant Act most schools, even ones that weren't land grant schools, had some form of compulsory military training for all male students. This would largely involve basic drill and ceremony so the uniform depicted there would be appropriate for that. It's also possible that there is no military connotation and it is just a marching band uniform but that seems unlikely.

If you have more information about what year the picture was taken and how old your Great-great Grandfather was it could narrow it down a bit. Obviously if he didn't go to college my theory is incorrect.

It looks to me that he was in the Salvation Army. Look at this website and its images.

Do you know the approximate year the photo was taken?