All engines use oil, if your engine is not using oil then it is being replaced with fuel and blowby residue and water. It is entirely normal for an engine to burn oil, don't worry about it and just check it more regularly.
I actually found my engines burn less oil with synthetic. How long was it since you last checked your oil? 1/4 litre per 600 miles is normal and some manufacturers even say 1/2 litre per 600 miles is normal. When an engine stops using oil that is a sign of wear.
“She may not look like much, but she's got it where it counts, kid. I've made a lot of special modifications myself.”
— Han Solo