  We investigate the expected gravitational wave emission from coalescing
supermassive black hole (SMBH) binaries resulting from mergers of their host
galaxies. When galaxies merge, the SMBHs in the host galaxies sink to the
center of the new merged galaxy and form a binary system. We employ a
semi-analytic model of galaxy and quasar formation based on the hierarchical
clustering scenario to estimate the amplitude of the expected stochastic
gravitational wave background owing to inspiraling SMBH binaries and bursts
owing to the SMBH binary coalescence events. We find that the characteristic
strain amplitude of the background radiation is $h_c(f) \sim 10^{-16} (f/1 \mu
{\rm Hz})^{-2/3}$ for $f \lesssim 1 \mu {\rm Hz}$ just below the detection
limit from measurements of the pulsar timing provided that SMBHs coalesce
simultaneously when host galaxies merge. The main contribution to the total
strain amplitude of the background radiation comes from SMBH coalescence events
at $0<z<1$. We also find that a future space-based gravitational wave
interferometer such as the planned \textit{Laser Interferometer Space Antenna}
({\sl LISA}) might detect intense gravitational wave bursts associated with
coalescence of SMBH binaries with total mass $M_{\rm tot} < 10^7 M_{\odot}$ at
$z \gtrsim 2$ at a rate $ \sim 1.0 {\rm yr}^{-1}$. Our model predicts that
burst signals with a larger amplitude $h_{\rm burst} \sim 10^{-15}$ correspond
to coalescence events of massive SMBH binary with total mass $M_{\rm tot} \sim
10^8 M_{\odot}$ at low redshift $ z \lesssim 1$ at a rate $ \sim 0.1 {\rm
yr}^{-1}$ whereas those with a smaller amplitude $h_{\rm burst} \sim 10^{-17}$
correspond to coalescence events of less massive SMBH binary with total mass
$M_{\rm tot} \sim 10^6 M_{\odot}$ at high redshift $ z \gtrsim 3$.
