The foundations of the school were laid in 1999 with the formation of the Foundation (Yayasan) by Ibu Ace Robin and Ibu Sopantini with Lombok residents Peter Cranfield and Mark Heyward. The school opened on January 17th 2000 with six students and five teaching staff (three Indonesian and two international teachers). It grew steadily over the first two years, with Ibu Sopantini as the founding principal. Work continued on consolidating curriculum planning, administrative systems and the professional development of teachers. Sekolah Nusa Alam was a founding member of the National Plus Schools Association, formed in Jakarta in 2000.

Enrolments grew to over 50 by the start of 2003. To accommodate the growth, land was acquired adjacent to the initial site. Over the following 14 years, additions were made including a sports hall, junior secondary classrooms and extensions to provide more classrooms, sports halls, science and computer labs, play areas and toilet facilities, a large parking area and a senior school block. Enrolments grew to 250.

In 2014 the school obtained its SPK licence and achieved SMA national accreditation obtained with a score of 92, and designation ‘Amat Baik’ (Excellent).

As the school entered its 18th year it began a new chapter, moving to a brand new purpose-built international campus on the outskirts of Mataram.

Between 2018 and 2022, SNA survived earthquakes and the COVID-19 pandemic, with enrolments rising to 170.