We systematically investigate the magnetic properties of Cu4-xZnx(OH)6FBr using the neutron diffraction and muon spin rotation and relaxation (μSR) techniques.Neutron-diffraction measurements suggest that the longrange magnetic order and the orthorhombic nuclear structure in the x =0 sample can persist up to x =0.23 and 0.43,respectively.The temperature dependence of the zero-field μSR spectra provides two characteristic temperatures,TAo and Tλ,which are associated with the initial drop close to zero time and the long-time exponential decay of the muon relaxation,respectively.Comparison between TAo and TM from previously reported magnetic-susceptibility measurements suggest that the former comes from the short-range interlayer-spin clusters that persist up to x =0.82.On the other hand,the doping level where Tλ becomes zero is about 0.66,which is much higher than threshold of the long-range order,i.e.,～0.4.Our results suggest that the change in the nuclear structure may alter the spin dynamics of the kagome layers and a gapped quantum-spin-liquid state may exist above x =0.66 with the perfect kagome planes.