The Argon Power Cycle engine is a novel concept for high efficiency and zero emission through the replacement of N2 by Ar. However, the higher in-cylinder temperature and pressure as by-products cause heavier knock. The anti-knock strategies, such as reducing compression ratio and retarding ignition time, offset the efficiency increased by the Argon Power Cycle. Therefore, knock control becomes the most urgent task for the Argon Power Cycle engine development. The anti-knock methods, including fuel replacement, ultra-lean combustion, high dilution combustion, and water injection, were considered. The simulated ignition delay times were used to evaluate the probability of knock. The Otto cycle, combined with chemical equilibrium, was utilized to confirm the effect on the thermal conversion efficiency and each in-cylinder thermodynamic state parameter. The results show that the ignition delay times increase by a factor of two when the Ar dilution ratio increases from 79% to 95%. With a compression ratio of nine and an Ar dilution ratio of 95%, the thermal conversion efficiency of the H2-fueled Argon Power Cycle is 70%. At temperature ranging from 800 to 1200 K, the ignition delay times increase by a factor of two when the excess oxygen ratio increases from 1.0 to 3.0. The autoignition inhibiting effect of fuel replacement rises with the increasing temperature. At 1200 K, the ignition delay times increase by a factor of 100 with H2 replaced by either CH4 or NH3. Additive steam has a negligible effect on ignition delay times. The H2-fueled Argon Power Cycle engine with a dilution ratio higher than 95% and an excess oxygen ratio of 3.0 seems to be the best design. CH4 and NH3 both have excellent anti-knock quality but should be applied with dedicated methods to eliminate CO, CO2, and NOx emissions introduced into Argon Power Cycle engines.