The suitability of indium gallium zinc oxide (IGZO) thin-film transistors (TFT) for implementation of active matrix display of organic light emitting diodes (AMOLED) compensation pixel circuits is addressed in this paper. In particular, the impact of mobility on compensating performance for the implementation in AMOLED pixel circuits is investigated. Details of the effective mobility modeling using the power law of gate-to-source voltage are provided, and parameters are extracted according to the measured current-to-voltage data of IGZO TFT samples. The investigated AMOLED pixel circuit consists of 4 switching TFTs, 1 driving TFT, and 1 capacitor. A " source-follower” structure is used for the threshold voltage extraction of the driving transistor. A new timing diagram is proposed; thus the current error of the pixel circuit is almost independent of the effective mobility. But, to improve the precision of the threshold voltage extraction of the driving transistor, the mobility is required to be greater than 5 cm²V^-1s^-1. On the other hand, the optimized storage capacitance is reversely proportional to the effective mobility. Thus, the layout area of the pixel circuit can be decreased from 100 × 100 to 100 × 68 μm², with the effective mobility increased from 10 to 50 cm²V^-1s^-1. Therefore, IGZO TFT is a good alternative backplane technology for AMOLED displays, and a higher effective mobility is preferred for high compensation performance and compact layout.