Positive Train Control Implementation and Financing Act of 2018 This bill amends federal transportation law to repeal provisions authorizing a railroad to include in any revised plan to implement a positive train control system an alternative schedule and sequence for implementing such system. Under current law, a railroad is required to submit a revised plan for implementing a positive train control system by December 31, 2018. The bill prohibits further extensions of such deadline. The Department of Transportation shall provide grants to entities providing regularly scheduled intercity or commuter rail passenger transportation to implement positive train control systems. An entity providing regularly scheduled intercity or commuter rail passenger transportation may not begin service on any new route unless a positive train control system is fully implemented and operational on such route. The bill requires the National Railroad Passenger Corporation (Amtrak) to provide a detailed status report on progress in implementing a positive train control system on each of its routes.