We investigated the back gate voltage (VBG) dependent electrical conductivity of Zn1-(y+x)(Al-x,Eu-y)O (x = 0.00, 0.01; y = 0.00, 0.01, 0.02 and 0.05) thin films. Zn1-(y+x)(Al-x,Eu-y)O (x = 0.00, 0.01; y = 0.00, 0.01, 0.02 and 0.05) thin films were synthesized with combining sol-gel and spin coating techniques. Electrical conductivity measurements was monitored by longitudinal conductivity curves of Eu doped (Zn, Al)O thin films. The measurements show a sharp decrease or increase in conductivity of Eu doped (Zn, Al)O thin films by an applied +/- V-BG, which was not observed for Al doped ZnO thin films. The Eu amount in (Zn, Al)O lattice was the key parameter to manage the change in conductivity by +/- V-BG. The highest increase in conductivity by applied +/- V-BG was observed for 1 mol% Eu-doped Zn1-(y+0.01)(Al-0.01,Eu-y)O films, which also performed the highest longitudinal conductivity without a V-BG. By applied V-BG = 100 V, the change ratio in conductivity reached up to 436% for 1 mol% Eu doped (Zn, Al)O thin films. The response to VBG were drastically decreased by increase in Eu amounts in the lattice, and furthermore no change in conductivity was observed for 5 mol% Eu doped (Zn, Al) O thin films.