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Trained at the Trustees Academy and the RSA Life School 1896 to 1899. Commenced his artistic career as a lithographic illustrator. He was also art advisor to the publishing firm of Messrs Nelson & Sons. He is best known for his strong figure paintings but also produced flower paintings. He taught at Edinburgh College of Art until 1924. Grieve exhibited at the RSA from 1895 until 1937. He became an Associate Member of the RSA in 1920 and an Academician in 1929.