Transparent and stretchable conductors are essential components in many stretchable electronics. However, it is still a challenge to make this kind of conductor easily and cost-effectively. Here, a way to utilize cross-stacked superaligned carbon nanotube films to make transparent and stretchable conductors is reported. The as-produced cross-stacked films are isotropic in electrical conductivity, but anisotropic in mechanical properties, because of their microscale cross structures. Along some directions, the films can sustain a high strain, of more than 35%, which is helpful for applications as stretchable conductors. These cross-stacked films can be further made into composite films with polyvinyl alcohol by a dip-coating method, and with polydimethylsiloxane by an embedding method. The former composite films have similar isotropic electrical and anisotropic mechanical properties to SACNT films, but much larger capability in terms of tensile load. The latter composite films possess quite highly stretchable and reversible electrical behaviors, which can be used in stretchable touch panels, solar cells, strain sensors, and implanted conductors.