We report the coexistence of bulk superconductivity with T(c)=3.8 K and charge density wave (CDW) in Cu intercalated quasi-two-dimensional crystals of ZrTe(3). The Cu intercalation results in the expansion of the unit cell orthogonal to the Zr-Zr metal chains and partial filling of CDW energy gap. We present anisotropic parameters of the superconducting state. We also show that the contribution of CDW to the scattering mechanism is anisotropic in the a-b plane. The dominant scattering mechanism in the normal state for both ZrTe(3) and Cu(0.05)ZrTe(3) along the b axis is the electron-electron umklapp scattering.