The aim of this research is to develop a novel design of interval type-2 neuro-fuzzy (IT2NF) controller for active vibration control of a flexible structure during an earthquake. For this purpose, two adaptive neural network based fuzzy logic controllers are designed and combined to create the novel design of an IT2NF controller to reduce the vibrations of two-storey flexible building model that occur during earthquake disturbance effects. Accordingly, dynamic modeling of a flexible structure is realized and simulated using the MATLAB / SimMechanics. Then, an experimental setup consisting of two-storey flexible structure, active mass damper (AMD) and shaker is established. Additionally, IT2NF controller is implemented in simulation and experimental models, and the effectiveness and performance of the IT2NF controller are tested under the scaled Northridge Earthquake acceleration. The obtained simulations and experimental responses are evaluated in terms of cart displacements, deflections, and accelerations of the flexible floors showing a good agreement between the simulations and the experimental results. The results show that the designed novel IT2NF controller reduced the total deflections of first and second floor by 72.3% and 68.7%, respectively, when compared with the uncontrolled system. Additionally, it is also found that the designed IT2NF controller is able to reduce the accelerations of the first and second floor by 64.8% and 54.6%, respectively. The proposed and designed control method reported in this study can be employed as an active vibration controller for multi-degree of freedom of flexible systems under the disturbances such as earthquake excitations.