Add the water to a saucepan over a high heat and bring to the boil.
Matcha has a tendency to clump, so to avoid this happening, add the matcha green tea powder to a small bowl along with 2 tablespoons of the boiled water and stir or whisk to dissolve the powder. Set aside.
Stir the sugar into the pot of boiling water, then reduce the heat and simmer for about 5 minutes until the sugar has dissolved, stirring occasionally.
Whisk the dissolved matcha into the sugar syrup. Set aside to infuse and cool slightly for 10 minutes.
Place the fine mesh sieve over a bowl, and strain the matcha syrup into it to remove any undissolved matcha. You can skip this step if there are no clumps of matcha powder.
Allow the syrup to cool completely, then pour into a clean jar or bottle.
Store the matcha simple syrup in the refrigerator. It should keep for about 1-2 weeks.