Gravitational waves from the pulsar glitch can be detected by next generation gravitational wave observatories. We investigate characteristics of the modes that can emit the gravitational waves excited by three different types of perturbations satisfying conservation of total rest mass and angular momentum. These perturbations mimic the pulsar glitch theories i.e., change of moment of inertia due to the star quakes or angular momentum transfer by vortex unpinning at crust-core interface. We carry out numerical hydrodynamic simulations using the pseudo-Newtonian method which makes weak field approximation for the dynamics, but taking all forms of energies into account to compute the Newtonian potential. Unlike other works, we found that the first and second strongest modes that give gravitational waves are $^2p_1$ and $H_1$ rather than$^2f$. We also found that vortex unpinning model excites the inertial mode in quadrupole moment quite effectively. The inertial mode may evolve into the non-axisymmetric r-mode.