Access to Substance Abuse Treatment Act of 2018 This bill amends the Public Health Service Act to require the Center for Substance Abuse Treatment to award grants to federally qualified health centers, substance abuse treatment centers, rehabilitation treatment centers, and residential treatment centers to expand access to evidence-based and cost-effective substance abuse treatment services. Priority for grants must be given to centers and programs: (1) serving communities with a greater incidence of substance abuse; or (2) providing, or proposing to incorporate, medication-assisted treatment. Services must be delivered in a manner reflecting person-centered care.