  We present a newly developed cosmological hydrodynamics code based on
weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation
laws. WENO is a higher order accurate finite difference scheme designed for
problems with piecewise smooth solutions containing discontinuities, and has
been successfully applied for problems involving both shocks and complicated
smooth solution structures. We couple hydrodynamics based on the WENO scheme
with standard Poisson solver - particle-mesh (PM) algorithm for evolving the
self-gravitating system. The third order low storage total variation
diminishing (TVD) Runge-Kutta scheme has been used for the time integration of
the system. To test accuracy and convergence rate of the code, we subject it to
a number of typical tests including the Sod shock tube in multidimensions, the
Sedov blast wave and formation of the Zeldovich pancake. These tests validate
the WENO hydrodynamics with fast convergence rate and high accuracy. We also
evolve a low density flat cosmological model ($\Lambda$CDM) to explore the
validity of the code in practical simulations.
