Preheat oven to 350°F (175°C). Grease a loaf pan.
In a mixing bowl, combine flour, sugar, baking powder, baking soda, and salt.
In another bowl, mix eggs, oil, vanilla extract, and lemon zest.
Add wet ingredients to dry ingredients and stir until just combined.
Fold in shredded zucchini.
Pour batter into prepared loaf pan.
Bake for 45 minutes or until a toothpick inserted into the center comes out clean.
Let cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.