The club was founded in 1980 and was Brava's first club, the club name's etymology is the nickname for Cape Verde Ilhas de morabeza. Morabeza is the Portuguese word for hospitality and Ilhas de morabeza means the "Islands of hospitality"'. Their first appearance was in 1982 and won four straight in 1985.
In 1982, no national championships took place due to the 1982 Amílcar Cabral Cup taking place in Praia's stadium now Estádio da Várzea, they played the first national cup which ended in a loss to São Vicente's CS Mindelense. Later, they had the first three appearances in the national championships, their first was in 1981 or 1982, their fourth straight was in 1985 where club headed to the finals and lost to Sporting Praia. Their first more island titles including their fifth in 1992 and later headed to the nationals, their fifth was in 2005. Their second was in 2005 where they defeated the Longstanding Nô Pintcha who won the most titles, the club was placed in Group B and did not won a match. For their next four appearances, the club only played in the group stage. Again the club was in Group B in 2007 and Morabeza had only two draws with in the last two weeks with Maio's Académica da Calheta and São Nicolau's Ultramarina. In 2008, they were for the third time in Group B and made their first win of the century in the first round where they defeated Santiago North's Estrela dos Amadores 2-0, then they defeated Fogo's Vulcânicos 2-0 in the second round, in the third round, a scoreless draw was made with Boa Vista's Académica Operária, they had the highest point numbering seven. In 2010, after their second consecutive win for the island, the club had their last national appearnance and was placed in Group A for the 2010 season, the first match with Boavista was a scoreless draw in the first round, then Morabeza had their only loss with Marítimo do Porto Novo. Morabeza's only win was over Solpontense 3-1 on May 23. The remaining two matches had a goal draw with Batuque and Botafogo.
Recently, their positions was slipping in the last three seasons in 2016, they were 4th in 2014, 5th in 2015, each with only four wins but in the 2016 season Morabeza finished 6th had a win and the club with 10 losses, scored 12 goals and conceded 50 goals.
Morabeza started second for the 2016-17 Brava season with a win over once successful Juventude da Furna, then third, then at the third round second behind Sporting after their win over Benfica,. They had their bye week for the fourth round, Sporting defeated Morabeza 1-4 on February 18 and lost a position to fourth along with their chance for another regional title. They returned to third place with a win over Nô Pintcha. On April 2, they defeated Corôa in the 11th round match, Académica scoring a higher match placed Morabeza fourth where they would finish. Their last appearance and win was 4-0 over Corôa on April 24. The unexpected came as Morabeza did not played in a final match against Académica, the region awarded 3-0 against the club. Morabeza had 17 points, 5 wins and 23 goals, fourth ranked in the region.
Morabeza alongside Benfica Brava were the two clubs who played in a special competition known as Taça de Beneficiência (the Beneficience Cup, or the Goodwill Cup), Morabeza won the special title in 2017.