The Indian Ocean Dipole (IOD) affects weather and climate in many parts of the world, but a realistic simulation of the IOD in state-of-the-art climate models remains a challenge. In most models, IOD peak-season amplitudes are systematically larger than that of the observed, a bias that deterministically affects climate projections in IOD-affected regions. Understanding the cause of this bias is therefore essential for alleviating model errors and reducing uncertainty in climate projections. Here it is shown that most Coupled Model Intercomparison Project Phase Three (CMIP3) and CMIP5 models produce too strong a Bjerknes feedback in the equatorial Indian Ocean, leading to the IOD bias. The thermocline-sea surface temperature (SST) feedback exerts the strongest influence on the simulated IOD amplitude; models simulating a stronger thermocline-SST feedback systematically generate a greater IOD amplitude. The strength of the thermocline-SST feedback in most models is predominantly controlled by the climatological west-east slope of the equatorial thermocline, which features an unrealistic mean slope tilting upward toward the eastern Indian Ocean. The unrealistic thermocline structure is accompanied by too strong a mean easterly wind and an overly strong west-minus-east SST gradient. The linkage of the mean climatic conditions, feedback strength, and projected climate highlights the fundamental importance of realistically simulating these components of the climate system for reducing uncertainty in climate change projections in IOD-affected regions.