A novel inbred maize line designated PHB1V and seed, plants and plant parts thereof. Methods for producing a maize plant that comprise crossing inbred maize line PHB1V with another maize plant. Methods for producing a maize plant containing in its genetic material one or more traits introgressed into PHB1V through backcross conversion and/or transformation, and to the maize seed, plant and plant part produced thereby. Hybrid maize seed, plant or plant part produced by crossing the inbred line PHB1V or an introgressed trait conversion of PHB1V with another maize line. Inbred maize lines derived from inbred maize line PHB1V, methods for producing other inbred maize lines derived from inbred maize line PHB1V and the inbred maize lines and their parts derived by the use of those methods.