In this paper, we introduce the notion of weak filters in quasi-pseudo-BL algebras. First, we discuss the properties of weak filters of a quasi-pseudo-BL algebra and characterize the weak filters generated by some non-empty subsets. Second, we investigate the relationship between weak filters of a quasi-pseudo-BL algebra and filters of its pseudo-BL subalgebra. Moreover, we study some kinds of weak filters such as normal, prime, maximal and weak prime weak filters. Third, the quotient quasi-pseudo-BL algebras with respect to normal weak filters are defined and the relation between (weak) filters of a quasi-pseudo-BL algebra and (weak) filters of its associated quotient algebra is discussed. Finally, we present the topological properties of the set of all prime weak filters of a quasi-pseudo-BL algebra and show that the prime spectrum is a complete T0 topological space.