To study the compressive mechanical properties of a new type of brazed aluminum honeycomb plate (BAHP), tensile tests on single- and brazed-cell walls as well as compression tests in the out-of-plane, in-plane longitudinal, and transverse directions were conducted. Compared to the material properties of a traditional glued aluminum honeycomb plate (GAHP), those of the single- and brazed-cell walls of the BAHP are entirely different. Therefore, their characteristics should be considered separately when performing theoretical and simulation analysis. Under out-of-plane compression, the core of the BAHP did not debond, owing to its higher strength than that of the GAHP. In comparison, under in-plane compression in the longitudinal and transverse directions, the load–displacement characteristics, ultimate load, and failure modes also differed, and there was no large-scale cracking. Considering the characteristics of the BAHP, a strength prediction method was proposed. The simulation results demonstrated that the model built based on the new method was highly consistent with the experimental results. Defects with uneven height and debonding will cause the overall instability, and the degree of defects will influence the strength and instability displacement, which have little impact on the elastic stage. Moreover, the model considering defects is closer to the test results.