In this study, the buckling and compressive failure of adhesively-bonded stepped-lap joints (with/without composite patches) composed of pultruded glass fiber-reinforced polymer composite laminates was investigated experimentally and numerically. Two-component epoxy adhesive was used for bonding purposes. Composite patches were woven glass-epoxy layer. They were added onto the conventional stepped-lap joints so that additional load transfer paths were created and localized stress concentrations near joint edge were reduced. The axial compression tests were performed and the results revealed that the buckling and failure load of new stepped lap composite joints with composite patches were significantly higher than the conventional stepped lap joints. The influence of the overlap length was evaluated. For both types of joints, a small increase was observed in failure loads by increase of the overlap length. Numerical results showed a very good agreement with experimental results.