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The couplings of the Higgs boson ($H$) with massive gauge bosons of weakinteraction ($V= W, Z$), can be probed in single Higgs boson production at theproposed future Large Hadron-Electron Collider (LHeC). In the collision of anelectron with a proton, single Higgs production takes place via so-calledcharged-current ($e^-p \to \nu_e H j$) and neutral-current ($e^-p \to e^-H j$)processes. We explore the potential of the azimuthal angle correlation betweenthe forward jet and scattered neutrino or electron in probing the non-standard$HVV$ couplings at the collider center-of-mass energy of $\sqrt{s} \approx1.3$~TeV. We choose the most general modifications (of $CP$-even and $CP$-oddnature) to these couplings due to new physics effects beyond the standardmodel. We derive exclusion limits on new physics parameters of $HVV$ couplingsas a function of integrated luminosity at $95\%$ C.L. using the azimuthalangular correlations in charged- and neutral-current processes. We find thatusing 1000 $fb^{-1}$ data, the standard model-like new physics parameters in$HWW$ and $HZZ$ couplings can be constrained with accuracies of $4\%$ and$15\%$, respectively. The least constrained $CP$-even parameters of $HWW$coupling can be as large as 0.04, while those of $HZZ$ coupling can have valuesaround 0.31. Allowed values of $CP$-odd parameters in $HWW$ and $HZZ$ couplingsare found to be around 0.14 and 0.34, respectively. We also study changes inthe allowed values of non-trivial new physics parameters in the presence ofother parameters.

Probing non-standard $HVV (V=W, Z)$ couplings in single Higgs production at future electron-proton collider