Flexure-guided fast tool servo (FTS) driven by piezoelectric actuator (PEA) has the advantages of high accuracy and high speed, which makes it has been widely applied in the microstructure surface processing. Unfortunately, PEA has complicated hysteresis nonlinearity, which will greatly reduce the processing accuracy. The common PID and other traditional control methods are hard to handle complex hysteresis nonlinearity issue. As a classic method of intelligent hysteresis modeling, the traditional artificial neural network (TANN) algorithm can model the hysteresis nonlinearity accurately, however, the high-frequency dynamic hysteresis modeling based on TANN is difficult to be achieved on-line. Therefore, a novel on-line sequential extreme learning machine (OS-ELM) modeling method is proposed in this work. A compound control strategy consists of the OS-ELM model and PID feedback (OSEP) controller is proposed. A series of validation experiments are successfully carried out. The parameter identification results show that the training speed of the OS-ELM model is 836 times faster than that of the TANN model, and the identification accuracy is improved by 475 times. The closed-loop control results show that the positioning accuracy with OS-ELM hysteresis compensation is 13 times higher than with TANN model. It proves that the FTS system can achieve a satisfactory performance (stroke: 120μm, average linearity: 0.54%) under high closed-loop bandwidth 200Hz.