First, the definition of quantum weakest liberal precondition (termed wlp) wlp (A,B,C)-commutativity is proposed, some necessary, and sufficient conditions of wlp (A,B,C)-commutativity are presented. Secondly, it has been shown that wlp is not a healthy predicate transformer: it is verified that wlp is a weaker predicate transformer than the quantum weakest precondition (termed wp). The essential differences of wlp and wp are disclosed. Finally, the properties for sequential composition, parallel composition and block structure of wlp are investigated.