Lepton universality in tau-neutrino ($\nu_\tau$) scattering has been poorly tested. More precise measurement of the $\nu_\tau$ cross section would enable a search for new physics effects in $\nu_\tau$-nucleon CC interactions. Such measurement also has practical importance for next-generation neutrino oscillation experiments and astrophysical $\nu_\tau$ observations. The DsTau project has been proposed at CERN SPS to study tau-neutrino production with the aim of providing important data for future $\nu_\tau$ measurements. For $\nu_\tau$ cross section measurements, the practical method of producing an artificial $\nu_\tau$ beam employs the sequential decay of $D_s$ mesons produced in high-energy proton interactions. However, there has been no experimental measurement of the $D_s$ differential production cross section in fixed-target experiments using proton beams, which leads to a large systematic uncertainty on the $\nu_\tau$ flux estimation. The DsTau project aims to reduce this uncertainty in the current cross section measurement from about 50% to 10% by measuring the $D_s$ differential production cross section. For this purpose, emulsion detectors with a 50-nm spatial resolution will allow the detection of $D_s \rightarrow \tau \rightarrow X$ double kinks in a few mm range. Results from the beam tests conducted in 2016-2017 are presented together with a prospect for the pilot run in 2018 and the physics run in 2021.