Basedonafirstordernonlinearordinarydifferentialequationwithatmostasixth-degreenonlineartermwhichisextendedfromatypeofellipticequation,andbyconvertingitintoanewexpansionform,thispaperproposesanewalgebraicmethodtoconstructexactsolutionsfornonlinearevolutionequations.Beingconciseandstraightforward,themethodisappliedtomodifiedBenjamin-Bona-Mahony(mBBM)model,andsomenewexactsolutionstothesystemareobtained.Thealgorithmisofimportantsignificanceinexploringexactsolutionsforothernonlinearevolutionequations.