We study the prospects of measuring the CP property of the Higgs (h) coupling to tau leptons using the vector boson fusion (VBF) production mode at the high-luminosity LHC. Utilizing the previously proposed angle between the planes spanned by the momentum vectors of the (π+π0) and (π−π0) pairs originating in τ± decays as the CP-odd observable, we perform a detailed Monte Carlo analysis, taking into account the relevant standard model backgrounds, as well as detector resolution effects. We find that excluding a pure C mathcal{O}left(400 {mathrm{fb}}^{-1}right) luminosity at the 14 TeV LHC, and values of the CP-mixing angle larger than about 25° can be excluded at 95% confidence level using 3 ab−1 data. It is observed that the uncertainty in the angular resolution of the neutral pion momenta does not constitute a significant hurdle. Achieving a signal to background ratio (S/B) close to one, while keeping a high enough signal yield required to study the angular distributions selects out VBF as a promising mode to probe the CP nature of the hτ τ coupling, with gluon fusion suffering from a low S/B, and the W±h/Zh mode (with leptonically decaying W±/Z) having a much smaller signal rate.