Tuning of spin-orbit coupling and electron correlation effects in iridates by introducing electron or hole carriers can produce interesting physical phenomena. In this work, we experimentally investigate the electron/hole doping effect on magnetism and electrical transport in the canted antiferromagnetic (AFM) double perovskite La2ZnIrO6, where hole/electron doping are realized in two serial La2Zn1-x Li x IrO6 (0 ⩽ x ⩽ 0.35) and La2Zn1-y Ga y IrO6 (0 ⩽ y ⩽ 0.3) compounds, respectively. The x-ray photoelectron spectroscopy (XPS) reveals the existence of Ir5+ and Ir3+ oxide states in the Li+ and Ga3+ doped La2ZnIrO6. The magnetic susceptibilities and electron spin resonance (ESR) results reveal different responses between the Ir5+(5d4) and Ir3+ (5d6) ions in doped La2ZnIrO6, the Ir5+ ions have Van-Vleck paramagnetic contribution contrast to the completely nonmagnetic Ir3+ ions. Moreover, the Li+ doping cause more dramatic suppression of transition temperature (T N) and net ferromagnetic (FM) moments. All the Li+/Ga3+ doped samples remain Mott insulating state well fitted by the variable-range-hopping (VRH) transport mechanism. As a comparison, hole-doping is more effective to enhance the electrical conductivity than the case of electron, suggesting possible asymmetry of density of states nearby the Fermi level.