We report on the measurement of W-boson pair-production with the L3 detector at LEP at a centre-of-mass energy of 161.34 GeV. In a data sample corresponding to a total luminosity of 11 pb−1, we select four-fermion events with high invariant masses of pairs of hadronic jets or leptons. Combining all final states, the measured total cross section for W-pair production is: sigmaWW = 2.89+0.81-0.42(stat.) ± 0.14 (syst.) pb. Within the Standard Model, this corresponds to a mass of the W boson of: MW = 80.80+0.48-0.42 (exp.) ± 0.03 (LEP) GeV. Limits on anomalous triple-vector-boson couplings are derived.