In order to adjust the bandwidth of extremely narrow band filter, a novel hybrid acoustic-wave-lumped-element resonator(AWLR) filter is proposed in this paper. In this structure, the immittance inverter is introduced to adjust the bandwidth of the filter. The principle and criteria of its bandwidth adjustment are investigated. The parameter matrix of the two-port network is analyzed and the circuit network parameters before and after introducing into the immittance inverter are compared to obtain its criteria for adjusting the bandwidth. The simulation results after introducing different inverters are compared and verified. Taking the J-type inverter with J=1/123 as an example, the relative bandwidth of the filter is increased from 0.072% to 0.41% after introducing the inverter. The criteria for adjusting the bandwidth of hybrid AWLR filter are obtained and its correctness is verified.