How homochirality concerning biopolymers (DNA/RNA/proteins) could have originally occurred (i.e., arisen from a non-life chemical world, which tended to be chirality-symmetric) is a long-standing scientific puzzle. For many years, people have focused on exploring plausible physic-chemical mechanisms that may have led to prebiotic environments biased to one chiral type of monomers (e.g., D-nucleotides against L-nucleotides; L-amino-acids against D-amino-acids)-which should have then assembled into corresponding polymers with homochirality, but as yet have achieved no convincing advance. Here we show, by computer simulation-with a model based on the RNA world scenario, that the biased-chirality may have been established at polymer level instead, just deriving from a racemic mixture of monomers (i.e., equally with the two chiral types). In other words, the results suggest that the homochirality may have originated along with the advent of biopolymers during the origin of life, rather than somehow at the level of monomers before the origin of life.