  A family of type N exact solution of the Einstein's field equations, regular
everywhere except on the symmetry axis where it possesses a naked curvature
singularity, is present. The stress-energy tensor is of the anisotropic fluid
coupled with pure radiation field satisfy the different energy conditions and
the physical parameters diverge $r \rightarrow 0$. The space-time admitting a
non-expanding, non-twisting, and shear-free geodesic null congruence and
belongs to a special class of type N Kundt metrics. The space-time is
geodesically complete along the radiation direction in the constant $z$-planes
and exhibits geometrically different properties from the known pp-waves. The
present family of solution admits closed time-like curves (CTC) which appear
after a certain instant of time and the space-time is a four-dimensional
generalization of the Misner space metric in curved space-time.
