Prevent Harmful Algal Blooms Act This bill directs the National Oceanic and Atmospheric Administration (NOAA) to designate organizations as National Centers of Excellence in Harmful Algal Bloom Research, Prevention, Response, and Mitigation. An algal bloom is a rapid growth of algae that may create toxic or hypoxic (severely low-oxygen) conditions that are harmful to humans, animals, aquatic ecosystems, and the economy. To be eligible for designation, an organization must be an institution of higher education, a government research agency, a nonprofit laboratory or other research entity, or a consortium of such institutions; have demonstrated expertise and success in harmful algal bloom research, monitoring, forecasting, prevention, or response efforts; have demonstrated ability to collaborate with local, state, territorial, and tribal governments and federal agencies on harmful algal blooms; and be located in an area that is economically and environmentally impacted by harmful algal blooms. In designating National Centers of Excellence, NOAA must (1) consult with the Inter-Agency Task Force on Harmful Algal Blooms and Hypoxia; (2) ensure regional balance by designating centers in a variety of locations throughout the United States, including the District of Columbia, the Commonwealth of Puerto Rico, American Samoa, and other territories and possessions of the United States; and (3) avoid duplication of other harmful algal bloom research. Each designation shall be effective for five years and reviewed by NOAA in the fourth year of such effective period. The designation may be renewed for an additional five-year period.