Transgenic plants containing free amino acids, particularly at least one amino acid selected from among glutamic acid, asparagine, aspartic acid, serine, threonine, alanine and histidine accumulated in a large amount, in edible parts thereof, and a method of producing them are provided. In this method, glutamate dehydrogenase (GDH) gene is introduced into a plant together with a regulator sequence suitable for over expressing the sequence encoding GDH gene in plant cells.