In recent years, a.c servo motors have been gradually replacing d.c sevo motors in various high-performance demanded aplications such as machine tools and industrial robots. In particular, the high-performance slip-frequency control of an induction motor, which is often called the vector control, is considered one of the best a.c drive. In this paper, the transient state equation and vector control algrithms of an induction motor are described mathematically by using the two-axis theory(d-q coordinates). According to the result of these algorithms, we scheme the speed control system for an induction type ac servo motor in which vector control is adopted to give tha a.c motor high performance. Motor drive is a PWM inverter using power MOS-FET, and is controlled in order to let the actual input current of the motor track the current reference obtained from a microcomputer(8086 cpu). Driving experiments are performed in the range of 0 to 3000 rpm, and it is verified that high speed response is possible.