A thermoacoustic compressor is capable of converting an alternating gas flow to a direct one with a large pumping rate on the basis of the pressure oscillation nature of thermoacoustic engines and the flow rectification effect of check valves. Theoretical calculations are first carried out to study the factors that affect the performance of the closed and open thermoacoustic compression systems. It is shown that the frequencies of directly connected thermoacoustic engines should avoid small integer multiple relationships to operate efficiently. Increasing the pressure amplitudes is beneficial for the pressure lift in a closed system as well as the pumping rate in an open system. A demonstrative closed thermoacoustic compressor was then experimentally studied. A maximum average gas pumping rate of 4.55 Nm3/h during the first 2 s of the compression process was achieved when all components were at the same initial mean pressure of 2.13 MPa. The maximum pressure lift reached 0.4 MPa when the initial mean pressure was 2.4 MPa. It was found that the pressure lifts were roughly proportional to the pressure amplitudes. Due to the superposition of alternating and direct gas flows, deformation of pressure waveforms which has a negative effect on the performance was observed.