A test of CP invariance in Higgs boson production via vector-boson fusion using the method of the Optimal Observable is presented. The analysis exploits the decay mode of the Higgs boson into a pair of [Formula: see text] leptons and is based on 20.3 [Formula: see text] of proton-proton collision data at [Formula: see text] = 8 [Formula: see text] collected by the ATLAS experiment at the LHC. Contributions from CP-violating interactions between the Higgs boson and electroweak gauge bosons are described in an effective field theory framework, in which the strength of CP violation is governed by a single parameter [Formula: see text]. The mean values and distributions of CP-odd observables agree with the expectation in the Standard Model and show no sign of CP violation. The CP-mixing parameter [Formula: see text] is constrained to the interval [Formula: see text] at 68% confidence level, consistent with the Standard Model expectation of [Formula: see text].