A novel maize variety designated PH487H and seed, plants and plant parts thereof are provided. Methods for producing a maize plant comprise crossing maize variety PH487H with another maize plant are provided. Methods for producing a maize plant containing in its genetic material one or more traits introgressed into PH487H through backcross conversion and/or transformation, and to the maize seed, plant and plant part produced thereby are provided. Hybrid maize seed, plants or plant parts are produced by crossing the variety PH487H or a locus conversion of PH487H with another maize variety.