'quick' originates from Old English, specifically the word 'cwic', where 'cwic' meant 'alive, living'. 'grow' originates from Old English, specifically the word 'growan', where 'growan' meant 'to grow'. 'quick-growing' is a modern English compound formed from these elements.

'quick' entered Middle English (as 'quick[e]') with senses including 'alive' and later 'rapid'; 'grow' evolved from Old English 'growan' to Middle English 'growen' and modern English 'grow'. The compound 'quick-growing' developed in Modern English by combining 'quick' with the present participle 'growing'.

Initially, 'quick' often meant 'alive' and 'grow' meant 'to increase in size'; over time 'quick' shifted toward the sense 'rapid', so 'quick-growing' now means 'growing rapidly'.