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A new polarization-independent dual-wavelength fibre laser by fabricating a uniform FBG and a chirped FBG in a polarization-maintaining erbium-doped fibre (PM-EDF) is proposed and demonstrated.The wavelength spacing is 0.18nm and the optical signal-to-noise ratio is greater than 50dB with pump power of 246mW.Chirped FBG is used to make the reflectivity wavelengths of two PM-FBGs match easier.Since both EDF and FBGs are polarization-maintaining without splices and the two wavelengths are polarization-independent, the maximum amplitude variation and wavelength shifts for both lasing wavelength with 3-min intervals over a period of six hours are less than 0.2 dB and 0.005 nm, respectively, which shows stable dual-wavelength output.