Combine the peaches, water, and sugar in a medium-size saucepan. Bring to a boil and then reduce the heat to a simmer.
Stir to melt the sugar and let simmer about 10-15 minutes, until the peaches have softened and the mixture begins to thicken.
Place a fine mesh strainer over a bowl and pour the peach mixture through it, gently pressing on the peaches to extract as much liquid as possible.
Discard the peach remains and cool the syrup before transferring the syrup to an airtight container or jar. Store in the refrigerator until ready to use.