In this study, beech wood (Fagus silvatica L.) has been chemically modified with citric acid (Acidum citricum) and sodium hypophosphate (SHP) as the catalyst and gradually thermo-condensed in the dryer. Afterwards, wetting angle, surface energy, and shear strength of glued joints of modified and unmodified wood were determined. Testing of the bond strength according to standard EN 204 and comparison between modified and unmodified samples were executed. The adhesive used for bonding samples was polyvinyl acetate (PVAC), commonly used for gluing solid wood panels. Testing material was divided into three groups (dry, wet, and wet conditioned samples), within which statistical analysis was performed, and the significance of the differences between the modified and unmodified samples was determined. Surface energy is correlated with the bond strength, indicating that modification with citric acid negatively affects the adhesive properties of beech wood. A reduction in the bond strength of modified wood glued with PVAC glue compared to unmodified wood was determined. All the results indicate that the modified samples do not meet the minimum requirements for EN 204 bonded with PVAC glue. Therefore, it will be necessary to conduct further studies using other types of adhesives to investigate whether modified wood might be suitable for gluing.