Context.Low-mass X-ray binaries hosting a low-magnetised neutron star, which accretes matter via Roche-lobe overflow, are generally grouped into two classes called Atoll and Z sources after the path described in their X-ray colour-colour diagrams. Scorpius X–1 is the brightest persistent low-mass X-ray binary known so far, and it is the prototype of the Z sources.Aims.We analysed the firstNuSTARobservation of this source to study its spectral emission, exploiting the high-statistics data collected by this satellite. The colour-colour diagram shows that the source was probably observed during the lower normal and flaring branches of its Z track. We separated the data from the two branches in order to investigate the evolution of the source along the track.Methods.We fitted the 3−60 keVNuSTARspectra using the same models for the two branches. We adopted two descriptions for the continuum: in the first case, we used a blackbody and a thermal Comptonisation with seed photons originating in the accretion disc, and in the second case, we adopted a disc-blackbody and a Comptonisation with a blackbody-shaped spectrum of the incoming seed photons. A power-law fitting of the high-energy emission above 20 keV was also required in both cases.Results.The two models provide the same physical scenario for the source in the two branches: a blackbody temperature between 0.8 and 1.5 keV, a disc-blackbody with a temperature between 0.4 and 0.6 keV, and an optically thick Comptonising corona with an optical depth between 6 and 10 and a temperature about 3 keV. Furthermore, two lines related to the Kαand Kβtransitions of the He-like Fe XXVions were detected at 6.6 keV and 7.8 keV, respectively. A hard tail modelled by a power law with a photon index between 2 and 3 was also required for the two models.