Begin by whisking together melted butter, canola oil, eggs, and vanilla until combined. Add white and brown sugars and stir until the mixture is smooth.
Combine dry ingredients and then add them to the wet ingredients. You can either do this in a separate bowl, or just right on top of the wet ingredients.
Pour the batter into a prepared loaf pan and bake the zucchini bread on the lower rack in a preheated oven until a toothpick inserted in the center comes out clean.