Preheat the oven to 350°F (180°C). Line a 9x5-inch loaf pan with parchment paper.
In a large bowl, stir together zucchini, banana, sugar, oil, vanilla, and egg. In a medium bowl, whisk together flour, cinnamon, baking soda, and salt. Add the flour mixture to the zucchini mixture, and stir well to combine.
Spoon batter into prepared pan. Bake for 55-60 minutes until an inserted wooden spoon comes out clean. Cool in the tin for 10 minutes, then remove from the pan and cool on a wire rack.