Hydrogen peroxide takes much of the cost for Fenton reaction applied for treatment of organic contaminants. Therefore, the effective use of hydrogen peroxide makes the technology more cost effective. The effective use of hydrogen peroxide is especially needed in the soil and groundwater remediation where complete mixing is not possible and it takes a long time for reactive species to transport to the fixed target compounds. Stabilization ability for hydrogen peroxide of malonic acid was evaluated in Fenton and Fenton-like reactions in this study. Malonic acid contributes on the stabilization of hydrogen peroxide by weak interaction between iron and the stabilizer and inhibiting the catalytic role of iron. The stabilization effect increased as the solution pH decrease below the $pK_{a1}$. The stabilization effect increased as the concentration of malonic acid increased and the effect was maximized at the malonic acid concentration of about ten times higher than the iron concentration. The model organic contaminant was successfully oxidized in the presence of the stabilizer but the degradation rate was slower than the system without the stabilizer. The stabilization effect was also proved in a Fenton-like reaction where magnetite and hematite were used instead of soluble iron species.