Monte Carlo simulations were used to optimize the geometry of a mammography anti-scatter linear grid to achieve minimum scatter-to-primary ratio (SPR) for different X-ray tube voltages. A single optimum design of the grid with 0.9mm septa height, 12microm septa thickness and 100microm interspace thickness was found for breast phantom thicknesses between 30 and 80mm. The optimal grid has 0.153-0.330 scatter-to-primary ratio, a Bucky factor (BF) less than 2.5 and a contrast improvement factor (CIF) of 1.3.