In　this　paper,　we　investigate　the　potential　application　of　quantum　computation　for　constructing　pseudo-random　number　generators　(PRNGs)　and　further　construct　a　novel　PRNG　based　on　quantum　random　walks　(QRWs),　a　famous　quantum　computation　model.　The　PRNG　merely　relies　on　the　equations　used　in　the　QRWs,　and　thus　the　generation　algorithm　is　simple　and　the　computation　speed　is　fast.　The　proposed　PRNG　is　subjected　to　statistical　tests　such　as　NIST　and　successfully　passed　the　test.　Compared　with　the　representative　PRNG　based　on　quantum　chaotic　maps　(QCM),　the　present　QRWs-based　PRNG　has　some　advantages　such　as　better　statistical　complexity　and　recurrence.　For　example,　the　normalized　Shannon　entropy　and　the　statistical　complexity　of　the　QRWs-based　PRNG　are　0.999699456771172　and　1.799961178212329e-04　respectively　given　the　number　of　8　bits-words,　say,　16Mbits.　By　contrast,　the　corresponding　values　of　the　QCM-based　PRNG　are　0.999448131481064　and　3.701210794388818e-04　respectively.　Thus　the　statistical　complexity　and　the　normalized　entropy　of　the　QRWs-based　PRNG　are　closer　to　0　and　1　respectively　than　those　of　the　QCM-based　PRNG　when　the　number　of　words　of　the　analyzed　sequence　increases.　It　provides　a　new　clue　to　construct　PRNGs　and　also　extends　the　applications　of　quantum　computation.