  The anisotropy in the microwave conductivity of the ortho-II
YBa$_2$Cu$_3$O$_{6.50}$ is studied within the kinetic energy driven
superconducting mechanism. The ortho-II YBa$_2$Cu$_3$O$_{6.50}$ is
characterized by a periodic alternative of filled and empty $\hat{b}$-axis CuO
chains. By considering the CuO chain induced extended anisotropy impurity
scattering, the main features of the anisotropy in the microwave conductivity
of the ortho-II YBa$_2$Cu$_3$O$_{6.50}$ are reproduced based on the nodal
approximation of the quasiparticle excitations and scattering processes,
including the intensity and lineshape of the energy and temperature dependence
of the $\hat{a}$-axis and $\hat{b}$-axis microwave conductivities. Our results
also confirm that the $\hat{b}$-axis CuO chain induced impurity is the main
source of the anisotropy.
