Combine peach slices, water, and sugar in a medium saucepan.
Bring to boil over medium-high heat, then reduce to low heat and simmer, stirring occasionally. Simmer for 5 minutes until the sugar dissolves and the peaches start to break down.
Remove from heat and allow to cool for 15 minutes to bring your syrup to room temperature.
Place a fine-mesh strainer over a medium bowl. Carefully pour the mixture into the strainer, stirring the peaches gently to release any liquid.
Discard the cooked peaches or save them to go over vanilla ice cream or french toast.
Cool syrup completely before using. Store in a mason jar or other airtight container in the refrigerator for up to 2 weeks.