BACKGROUND: To move towards ending AIDS by 2030, HIV resources should be allocated cost-effectively. We used the Optima HIV model to estimate how global HIV resources could be retargeted for greatest epidemiological effect and how many additional new infections could be averted by 2030. METHODS: We collated standard data used in country modelling exercises (including demographic, epidemiological, behavioural, programmatic, and expenditure data) from Jan 1, 2000, to Dec 31, 2015 for 44 countries, capturing 80% of people living with HIV worldwide. These data were used to parameterise separate subnational and national models within the Optima HIV framework. To estimate optimal resource allocation at subnational, national, regional, and global levels, we used an adaptive stochastic descent optimisation algorithm in combination with the epidemic models and cost functions for each programme in each country. Optimal allocation analyses were done with international HIV funds remaining the same to each country and by redistributing these funds between countries. FINDINGS: Without additional funding, if countries were to optimally allocate their HIV resources from 2016 to 2030, we estimate that an additional 7·4 million (uncertainty range 3·9 million-14·0 million) new infections could be averted, representing a 26% (uncertainty range 13-50%) incidence reduction. Redistribution of international funds between countries could avert a further 1·9 million infections, which represents a 33% (uncertainty range 20-58%) incidence reduction overall. To reduce HIV incidence by 90% relative to 2010, we estimate that more than a three-fold increase of current annual funds will be necessary until 2030. The most common priorities for optimal resource reallocation are to scale up treatment and prevention programmes targeting key populations at greatest risk in each setting. Prioritisation of other HIV programmes depends on the epidemiology and cost-effectiveness of service delivery in each setting as well as resource availability. INTERPRETATION: Further reductions in global HIV incidence are possible through improved targeting of international and national HIV resources. FUNDING: World Bank and Australian NHMRC.