We started two observing programs with the Korean VLBI Network (KVN) monitoring changes in the flux density and polarization of relativistic jets in gamma-ray bright AGNs simultaneously at 22, 43, 86, 129 GHz. One is a single-dish weekly-observing program in dual polarization with KVN 21-m diameter radio telescopes beginning in 2011 May. The other is a VLBI monthly-observing program with the three-element VLBI network at an angular resolution range of 1.0--9.2 mas beginning in 2012 December. The monitoring observations aim to study correlation of variability in gamma-ray with that in radio flux density and polarization of relativistic jets when they flare up. These observations enable us to study the origin of the gamma-ray flares of AGNs.