The status of the experiment on the precise τ lepton mass measurement running at the VEPP-4M collider with the KEDR detector is reported. The mass value is evaluated from the τ + τ − cross section behaviour around the production threshold. The preliminary result based on 6.7 pb −1 of data is mτ = 1776.80 +0.25 −0.23 ± 0.15 MeV. Using 0.8 pb −1 of data collected at the ψ peak the preliminary result is also obtained: Γee ·Bττ (ψ ) = 7.2 ± 2.1 eV.