  Levy walk is a fundamental model with applications ranging from quantum
physics to paths of animal foraging. Taking animal foraging as an example, a
natural idea that comes to one's mind is to introduce the multiple internal
states for dealing with the dependence of the PDF of waiting time on the energy
of the animal and richness of the food at a particular location, etc; the
framework can also be used to model the moving trajectories of smart animals
without returning to the directions or locations which they come from
immediately. After building the Levy walk model with multiple internal states
and deriving the governing equation of the distribution of the positions of the
particles, some applications are discussed with specific transition matrices.
The type of diffusion for non-immediately-repeating L\'{e}vy walk is uncovered,
and the distribution and average of first passage time are numerically
simulated.
