Due to the discontinuity of Nomex honeycomb structure, it is challenging to evaluate its out-of-plane shear properties such as shear strength and shear modulus. The load-bearing capacity of the Nomex honeycomb is significantly influenced by its out-of-plane shear performance. Therefore, it is necessary to conduct investigations into the out-of-plane shear properties of Nomex honeycomb sandwich structures. In view of this, experimental investigations on the out-of-plane shear of Nomex honeycomb sandwich structures were conducted. The shear failure mode of the honeycomb core was identified via analysis of the deformation process of the Nomex composite sandwich structure. Constitutive relationships of Nomex honeycomb structures were obtained. Additionally, the influences of the thickness and the arrangement direction of honeycomb core on the shear strength, residual strength, and shear modulus were comparatively studied. The results showed that the Nomex composite sandwich structure with a thicker honeycomb core possesses lower shear strength. The impact of the thickness of honeycomb core on the residual strength was found to be negligible. For honeycombs of identical thickness, the sandwich structure with an L-directed core exhibited greater shear strength, shear modulus, and residual strength compared to those in the W direction.