Provided is a canola variety designated PV 581 GC and seed, plants and plant parts thereof produced from a cross of inbred varieties. Methods for producing a canola variety comprise crossing canola variety PV 581 GC with another canola plant. Methods for producing a canola plant containing in its genetic material one or more traits introgressed into PV 581 GC through backcross conversion and/or transformation, and to the canola seed, plant and plant part produced thereby are described. Canola variety PV 581 GC, the seed, the plant produced from the seed, plant parts and variants, mutants, and minor modifications of canola variety PV 581 GC are disclosed.