Sound propagation in a deep ocean two-axis underwater channel is often complex and difficult to simulate between surface channel and sound fixing and ranging (SOFAR) channel. The beam-displacement ray-mode (BDRM) theory is a normal mode method for propagation modeling in horizontally stratified shallow water. An improved method for computing the upper boundary reflection coefficient in the BDRM is proposed and applied to calculate the acoustic fields of a two-axis underwater channel. Transmission losses in the two-axis underwater channel are calculated in the new BDRM. The corresponding results are in good agreement with those from the Kraken code, and furthermore the computed speed of the new BDRM excels the other methods.