Iridates represent a unique material system that possesses both strong spin-orbit coupling and electron correlation. The interplay between spin-orbit coupling and correlation could facilitate the emergence of novel electronic and magnetic states. In this work, we report on a systematic study of magnetism in the double perovskite iridate La 2 ZnIrO 6 and its hole-doped compounds (La 1−x Sr x ) 2 ZnIrO 6 via dc magnetization measurement, heat capacity characterization, electron spin resonance spectroscopy, and simple modeling. Undoped La 2 ZnIrO 6 undergoes two magnetic transitions, at T 1 ∼ 7.3 K and T 2 ∼ 8.5 K, respectively. While magnetic hysteresis loops with large remnant moments are observed below these two transition temperatures, the corresponding magnetic states are shown to be canted antiferromagnetic by the linear increase in magnetization in the high field region along with the observation of antiferromagnetic resonance. The nature of the canted antiferromagnetic states with large canting angles can be understood by a simple model that includes both the Heisenberg exchange interaction and the Dzyaloshinskii-Moriya interaction. With the introduction of Ir 5+ by Sr 2+ doping, the canted antiferromagnetic phases are suppressed, accompanied by an enhancement of electrical conductivity.