Thinly slice the fennel bulb using a mandoline slicer or sharp knife.
Add the sliced fennel to a glass jar along with the garlic clove, peppercorns and anise seed.
Combine the water, vinegar, sugar, salt and lemon peel in a small sauce pot. Bring to a boil and stir until sugar and salt are dissolved.
Turn off heat and pour the liquid into the jar until just covering the fennel.
Let cool to room temperature then place the lid on the jar and transfer to the refrigerator. Pickled fennel will store in the refrigerator for up to 3-4 weeks.