In this article, measurements of the thermal conductivity of humid air as a function of pressure, temperature, and mole fraction of water, for pressures up to 5 MPa and temperatures up to 430 K, for different water contents (up to 10 % vapor mole fraction) are reported. Measurements were performed using a transient hot-wire apparatus capable of obtaining data with an uncertainty of 0.8 % for gases. However, as moist air becomes corrosive above 373 K and at pressures >5 MPa, the apparatus, namely, the pressure vessel and the cells had to be modified, by coating all stainless-steel parts with a titanium nitride thin film coating, about 4 μm thick, obtained by physical vapor deposition. The expanded uncertainty (coverage factor k = 2) of the present experimental thermal conductivity data is 1.7 %, while the uncertainty in the mole fraction is estimated to be better than 0.0006. Experimental details regarding the preparation of the samples, the precautions taken to avoid condensation in the tubes connected to the measuring cell, and the method developed for obtaining reliable values of the water content for the gas mixtures are discussed. A preliminary analysis of the application of the kinetic theory of transport properties in reacting mixtures to interpret the complex dependence of the thermal conductivity of humid air on water composition is addressed.