The compression of high-energy, linearly polarized pulses in a gas-filled hollow core fiber (HCF) by using a concentric phase mask is studied theoretically. Simulation results indicate that using a properly designed concentric phase mask, a 40-fs input pulse centered at 800 nm with energy up to 10.0 mJ can be compressed to a full width at half maximum (FWHM) of less than 5 fs after propagating through a neon-filled HCF with a length of 1 m and diameter of 500 μm with a transmission efficiency of 67％, which is significantly higher than that without a concentric phase mask. Pulses with energy up to 20.0 mJ can also be efficiently compressed to less than 10 fs with the concentric phase mask. The higher efficiency due to the concentric phase mask can be attributed to the redistribution of the transverse intensity profile, which reduces the effect of ionization. The proposed method exhibits great potential for generating few-cycle laser pulse sources with high energy by the HCF compressor.