In this paper, the GYRATOR circuit is designed by the highly linear MOS transconductor with the gain factor controllable by offset voltage, and the floating inductor, the floating resistor and the grounded resistor are simulated by the GYTATOR for VLSI. And for the design exmple, Butterworth filter is designed using this GYRATOR, and is conpensated by the frequency transformation for the frequency shift that due to non-ideal output impedance of transconductor.