We carry out the first detailed calculations of jet production associated with W gauge bosons in Pb+Pb collisions at the Large Hadron Collider (LHC). In our calculations, the production of W +jet in p+p collisions as a reference is obtained by Sherpa, which performs next-to-leading-order matrix element calculations matched to the resummation of parton shower simulations, while jet propagation and medium response in the quark-gluon plasma are simulated with the Linear Boltzmann Transport (LBT) model. We provide numerical predictions on seven observables of W +jet production with jet quenching in Pb+Pb collisions: the medium modification factor for the tagged jet cross sections I AA , the distribution in invariant mass between the two leading jets in N jets ≥ 2 events m jj , the missing p T or the vector sum of the lepton and jet transverse momentum | p M iss T |, the summed scalar p T of all the jets in an event S T , transverse momentum imbalance x jW , average number of jets per W boson R jW , and azimuthal angle between the W boson and jets ∆φ jW . The distinct nuclear modifications of these seven observables in Pb+Pb relative to that in p+p collisions are presented with detailed discussions.