A novel maize variety designated PHW3G and seed, plants and plant parts thereof. Methods for producing a maize plant that comprise crossing maize variety PHW3G with another maize plant. Methods for producing a maize plant containing in its genetic material one or more traits introgressed into PHW3G 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 variety PHW3G or a trait conversion of PHW3G with another maize variety. Inbred maize varieties derived from maize variety PHW3G, methods for producing other inbred maize varieties derived from maize variety PHW3G and the inbred maize varieties and their parts derived by the use of those methods.