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In the present work, a new assessment of the Al–Nb system, using a combined first-principle and CALPHAD approach, is presented. Formation enthalpies of all ordered configurations of the intermetallic phases (σ, D 0 22 and A 15) were estimated from ab initio calculations. The liquid, fcc and bcc phases are described by a substitutional solution model. The intermetallic phases D 0 22 and A 15 are described with the New Approach to the Compound Energy Formalism (NACEF). To model the σ phase, four descriptions are applied. In first, σ phase is described with the five-sublattice (5SL) model using combined CEF model where a modification was applied which allows to respect the formation enthalpies of end-members obtained from ab initio calculations. Then, a comparison with the results obtained using the NACEF approach applied to the five-sublattice (5SL), three-sublattice (3SL) and two-sublattice (2SL) models is presented. In all cases, assessments derived from the different descriptions of σ phase show very good agreement with the available experimental and ab initio data with a limited number of used parameters. In this sense, self-consistent thermodynamic descriptions of the Al–Nb system is provided. Moreover, this work shows from the example of the σ phase that the NACEF approach, contrary to what is commonly considered, allows the compatibility between different descriptions using different numbers of sublattices. This is particularly interesting for the construction of multi-component databases. [ABSTRACT FROM AUTHOR]