Combine sugar and water in a small saucepan and bring to a simmer, stirring to dissolve sugar. Add strawberries. Mash strawberries with a fork and let mixture simmer for 10 minutes.
Remove from heat and let cool. Pour mixture through a fine-meshed sieve into a bowl and press on mixture with a rubber spatula to get all liquid out.
Add 1/2 cup strawberry mixture to a pitcher along with lime juice and vodka. Stir well.