  This paper analyzes the error estimates of the hybridizable discontinuous
Galerkin (HDG) method for the Helmholtz equation with high wave number in two
and three dimensions. The approximation piecewise polynomial spaces we deal
with are of order $p\geq 1$. Through choosing a specific parameter and using
the duality argument, it is proved that the HDG method is stable without any
mesh constraint for any wave number $\kappa$. By exploiting the stability
estimates, the dependence of convergence of the HDG method on $\kappa,h$ and
$p$ is obtained. Numerical experiments are given to verify the theoretical
results.
