  Left-handed materials usually are realized in artificial subwavelength
structures. Here we show that some anisotropic superconductors, such as
$\mathrm{Bi_2Sr_2CaCu_2O_{8+\delta}}$, $\mathrm{YBa_2Cu_xO_y}$ and
$\mathrm{La_{2-x}Sr_xCuO_4}$, are intrinsic left-handed materials. The
condition is that the plasma frequency in the $c$ axis, $\omega_c$, and in the
$ab$ plane, $\omega_{ab}$, and the operating frequency, $\omega$, satisfy
$\omega_c<\omega<\omega_{ab}$. In addition $\omega$ should be smaller than the
superconducting energy gap to sustain superconductivity. We study the
reflection and transmission of electromagnetic waves, and reveal negative
refraction and backward wave with phase velocity opposite to the direction of
energy flux propagation. We also discuss possible approaches of improvement,
making these properties feasible for experimental validation. Being intrinsic
left-hand materials, the anisotropic superconductors are promising for
applications in novel electromagnetic devices in the terahertz frequency band.
