CERN-LHC. The production of W bosons is studied in proton-lead (pPb) collisions at a nucleon-nucleon centre-of-mass energy of $\sqrt{{s}_\textrm{NN}} = 8.16$ TeV. Measurements are performed in the $\textrm{W}^{\pm}\to\mu^{\pm}\nu$ channel using a data sample corresponding to an integrated luminosity of $173.4 \pm 8.7 \textrm{nb}^{-1}$, collected by the CMS Collaboration at the LHC. The number of positively and negatively charged W bosons is determined separately in the muon pseudorapidity region in the laboratory frame $|\eta_{\textrm{lab}}^{\mu}|<2.4$ and transverse momentum $p_{\textrm{T}}^{\mu}>25$~GeV/$c$. The $\textrm{W}^{\pm}$ boson differential cross sections, muon charge asymmetry, and the ratios of $\textrm{W}^{\pm}$ boson yields for the proton-going over the Pb-going beam directions are reported as a function of the muon pseudorapidity in the nucleon-nucleon centre-of-mass frame. The measurements are compared to the predictions from theoretical calculations based on parton distribution functions (PDFs) at next-to-leading-order. The results favour PDF calculations that include nuclear modifications and provide constraints on the nuclear PDF global fits.