Slender prismatic structures with inherently low damping can be prone to serious vibration excited by galloping. Extensive wind tunnel studies on galloping of vertical cantilevered structures exist in the literature, but none of those studies have covered a structure with an inclination to the wind. Structures are now designed with more complex and innovative architectural features and forms. It is obvious that wind flow around an inclined structure can be significantly different from that around a vertical structure. This paper presents the results from a program of wind tunnel study on the galloping effect of an inclined square cylinder. A single-degree-freedom model simulating the vibration of a slender structure in the transverse direction was designed and fabricated. A series of wind tunnel tests were conducted to study the galloping effect of the structure in terms of angle of wind incidence, inclination angle and structural damping ratio. The flow conditions being considered in this study were uniform smooth flow and turbulent flow conditions at a reduced wind velocity of 16. A mathematical model simulating the vibration of a slender structure in the transverse direction under smooth flow condition was also established with the measured wind tunnel test data. The predicted structural response by the mathematical model was then compared with the results from the wind tunnel tests. It is found that the effect of inclination angle is the most influencing factor affecting the response of structure in both smooth and turbulent wind conditions.