We have developed an all-optical fiber link antenna measurement system for a millimeter wave 5th generation mobile communication frequency band around 28 GHz. Our developed system consists of an optical fiber link an electrical signal transmission system, an antenna-coupled-electrode electric-field (EO) sensor system for 28GHz-band as an electrical signal receiving system, and a 6-axis vertically articulated robot with an arm length of 1m. Our developed optical fiber link electrical signal transmission system can transmit the electrical signal of more than 40GHz with more than -30dBm output level. Our developed EO sensor can receive the electrical signal from 27GHz to 30GHz. In addition, we have estimated a far field antenna factor of the EO sensor system for the 28GHz-band using an amplitude center modified antenna factor estimation equation. The estimated far field antenna factor of the sensor system is 83.2dB/m at 28GHz.