The Poisson's ratio describes an extent of transverse deformation of a material when an axial strain is applied. A change of the Poisson's ratio from positive to negative can equip a material with a set of specific properties. In this paper, a study of a composite material with a tunable Poisson's ratio is presented. Samples of such a composite were first fabricated with two different polymers based on a composite structure proposed in our previous work using a multi-material additive-manufacturing system. Using both experimental and numerical methods, deformation mechanisms and mechanical properties of this composite material were analyzed. The obtained results demonstrate that its Poisson's ratio can be reduced by increasing the difference in stiffness of constituent materials and turned from positive to negative when this difference is sufficiently high. Additionally, the study also validates a possible method to fabricate composites with designed structures and multi-constituent materials using additive-manufacturing techniques.