Block-based　prediction-quantization　hybrid　coding　framework　is　widely　used　in　video　compression,　which　results　in　visually　annoying　artifacts,　i.e.,　blocking　artifacts,　on　encoded　videos.　They　significantly　degrade　the　Quality-of-Experience　(QoE).　To　improve　the　QoE,　it　is　crucial　to　develop　Video　Quality　Assessment　(VQA)　methods　that　can　identify　and　quantify　various　artifacts,　among　which　the　negative　effect　introduced　by　blocking　artifacts　is　of　guiding　significance.　To　evaluate　and　monitor　video　quality　effectively,　a　novel　Blocking-based　Compressed　Video　Quality　Assessment　(BCVQA)　is　proposed　in　this　paper.　The　key　idea　of　the　BCVQA　method　is　a　blocking　detection　model　based　on　Just-Noticeable-Difference　(JND)　mechanism,　which　is　aimed　to　improve　detection　performance,　since　it　only　focuses　on　the　observable　blocking　artifacts.　Furthermore,　the　saliency　model　is　utilized　in　quality　prediction　procedure　after　blocking　detection,　considering　the　visual　attention　mechanism.　With　the　fusion　of　the　above　two　visual　mechanisms,　quality　prediction　of　compressed　videos　becomes　more　effective,　since　the　useful　information　is　refined　in　our　framework.　Experimental　results　show　that　the　proposed　BCVQA　is　consistent　with　perceived　quality　and　can　effectively　evaluate　video　quality.　©　2021　IEEE.