Grêmio Foot-Ball Porto Alegrense (Brazilian Portuguese pronunciation: [ˈɡɾemi.u futʃiˈbɔw ˌpoʁtwaleˈɡɾẽsi]), commonly known as Grêmio, is a Brazilian professional football club based in Porto Alegre, the capital city of the Brazilian state of Rio Grande do Sul. The club plays in the Campeonato Brasileiro Série A, the first division of the Brazilian football league system, and the Campeonato Gaúcho, Rio Grande do Sul's top state league. The club was founded in 1903 by businessman Cândido Dias da Silva and 32 other men, mostly from the large community of German immigrants of Porto Alegre.

Grêmio's home stadium is the Arena do Grêmio, which the team moved to in 2013. With a capacity of over 55,000, the stadium is one of the most modern venues in South America and the eight-largest of its kind in Brazil. Prior to that, Grêmio played at Estádio Olímpico Monumental since 1954. Grêmio usually plays in a tricolor (blue, black, and white) striped shirt, black shorts, and white socks, which originated the team's nickname.

In 1983, Grêmio became champions of the Intercontinental Cup after defeating Hamburger SV 2-1. Additionally, Grêmio is tied with São Paulo, Santos, Palmeiras, and Flamengo for the most Copa CONMEBOL Libertadores de América titles among Brazilian clubs, having won a total of three each.

In 2017, Grêmio was ranked first in the CBF club rankings and is listed by Forbes as the third most valuable football club in the Americas with an estimated value of $295.5 million. Grêmio has won 43 Campeonato Gaúcho, 2 Campeonato Brasileiro Série A, 1 Campeonato Brasileiro Série B, 1 Supercopa do Brasil, 1 Copa Sul, and 5 Copa do Brasil. Internationally, Grêmio has won 1 Intercontinental Cup, 3 Copa Libertadores de América, 2 Recopa Sudamericana, and 1 Sanwa Bank Cup.

Grêmio has a long-standing and intense rivalry with Internacional, widely regarded as one of the fiercest in Brazil and around the world. Matches between the two clubs are known as Grenais, or Grenal in singular form.