a person who displays or demands of others pointlessly precise conformity, fussiness about trivialities, or exaggerated propriety, esp. in a self-righteous or irritating manner.

adjective

bluenosed , old-maidish , precise , prim , prissy , proper , prudish , puritanical , strait-laced , stuffy , victorian , complacent , pompous , smug , straitlaced , vain