H.R.3404: To amend the Public Health Service Act to provide grants for the training of graduate medical residents in preventive medicine and public health.

Preventive Medicine and Public Health Training Act - Amends the Public Health Service Act to authorize the Secretary of Health and Human Services, acting through the Director of the Centers for Disease Control and Prevention (CDC), to award grants to or enter into contracts with certain eligible entities to provide training to graduate medical residents in preventive medicine specialties.

Requires grant funds to be used for: (1) residency programs for preventive medicine or public health; (2) financial assistance to resident physicians who plan to specialize in preventive medicine or public health; (3) preventive medicine or public health program costs, including curriculum development and practicum costs; and (4) the improvement of academic administrative units.