Carbonate materials at the site of the excavation in Petralona Cave have been dated with Electron Spin Resonance (ESR). The archaeological dose by ESR was tentatively converted to the age. The age and the average growth rate of the cave floor have been determined to be around 70,000 and 0.9 micrometer per year. The age of the middle travertine, the old cave floor excavated and the carbonate above the skeleton of Petralona man are around 350,000 years using the annual dose of 0.2 Rad/yr. The ages might be around 700,000 years if the dose is 0.1 Rad/yr.