The sixth-order accurate phase error flux-corrected transport numerical algorithm is introduced, and usedto simulate Kelvin-Helmholtz instability. Linear growth rates of the simulation agree with the linear theories of Kelvin-Helmholtz instability. It indicates the validity and accuracy of this simulation method. The method also has goodcapturing ability of the instability interface deformation. The sixth-order accurate phase error flux-corrected transport numerical algorithm is introduced, and used to simulate Kelvin-Helmholtz instability. Linear growth rates of the simulation agree with the linear theories of Kelvin-Helmholtz instability. It indicates the validity and accuracy of this simulation. method. The method also has goodcapturing ability of the instability interface deformation.