We propose the muon spin relaxation experiments at zero field and at longitudinal fields of Cu-based double perovskites Sr2Cu(Te1-xWx)O6 (x = 0.05, 0.08, 0.1) in order to clarify the nature of the wide range of the disordered phase including the quantum spin liquid state. From the magnetic susceptibility and the previous muon spin relaxation experiments, we confirmed the occurrence of a long-range antiferromagnetic order at 18 K for x = 0.05 and a quantum disordered state for x = 0.1. Those findings strongly suggest that The putative quantum critical point is expected to be around x = 0.08. From the investigations on three suggested compounds, we expect to draw the complete landscape of a quantum phase transition from the Neel antiferromagnetic order to the disordered state as well as to understand the quantum critical behavior in the view of the spin dynamics.