Glued laminated beams are used for construction purposes. They need to be connected with steel parts. Instead of screws, adhesive can be used to increase joint stiffness. This research study focused on the quality of the polyurethane adhesive bond between wood and steel. Three different one-component polyurethane adhesives were used: COSMO PU–100.110, COSMO PU–180.150, and COSMO PU–190.110. The wooden lamellas were fashioned from spruce wood and bonded with steel lamellas. For six days, the test specimens were exposed to different conditions: standard climate, moist climate, and soaking in water. A test of the tensile shear strength of lap joints, determining the wood failure percentage, was performed according to the SIST EN 205:2003 standard. The quality of the adhesive bond between the steel and wood depended on the polyurethane adhesive used. The best results were achieved with COSMO PU–190.110, which after exposure to the standard climate reached a shear strength of 8.49 N/mm2 and 53% wood failure. The preparation of the test specimens prior to the test also affected the quality of the adhesive bond. The best results were achieved by the test specimens exposed to the standard climate; the worst results by those soaked in water. The COSMO PU–190.110 and COSMO PU–180.150 adhesives proved to be useful for bonding steel and wood in dry conditions (standard climate). In contrast, the COSMO PU–100.110 adhesive proved to be useless for bonding steel and wood in the studied conditions.