It’s a scientific consensus that carbon nanotube (CNT) with outstanding mechanical and physical performance compared with traditional carbon fiber has great potential on the development of next generation advanced composite materials. Like the way that carbon fibers reinforce the matrix, the alignment of CNTs can also be realized in the matrix, which indicates that the material properties of carbon nanotube reinforced composite (CNTRC) can be customized to achieve large anisotropicity. In this paper, the design and optimization of stacking sequences of CNTRC laminates will be investigated through theoretical and numerical methods to obtain out-of-plane negative Poisson’s ratio (NPR), which is an anomalous material property enabled by the large anisotropicity. The out-of-plane Poisson’s ratios of a CNTRC laminate can be derived based on an extended classical laminate theory (CLT), where the out-of-plane strain and stress are also included. The proposed theoretical method is verified by the comparison with three-dimensional finite element results. Through theoretical analysis of various stacking sequence, we can design and optimize the auxetic properties for CNTRC laminates. Furthermore, the von-Karman type dynamic equations of a laminate beam are also derived in the frame work of Reddy’s shear deformation theory and solved by means of a two-step perturbation technique. To study the low-velocity impact response of auxetic CNTRC laminate beams, the motion equation of the impactor is also taken into account. The contact process is estimated by a modified Hertz model where the effect of out-of-plane Poisson’s ratio is included. The governing equations for both the beam and impactor are numerically calculated by Runge-Kutta method. Finally, the effects of NPR as well as CNT volume fraction on the low-velocity impact response of CNTRC laminate beam are studied and discussed.