  In this paper, we forecast the expected detection rates and redshift
distributions of gravitationally lensed gravitational waves (GWs) from three
different mass distributions of primordial black holes (PBHs) and two stellar
formation models of astrophysical black holes (ABHs) in the context of
DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) and it's
smaller scale version B-DECIGO. It suggests that DECIGO will be able to detect
$10^4-10^5$ GW signals from such binary black holes (BBHs) each year and the
event rate distributions for PBHs will differ from those for ABHs due to their
different merger rate with respect to redshift. The large number of event rates
make $5-100$ detections of lensed GW signals being possible. After considering
the gravitational lensing effect, the difference between the detection rates
and distributions for PBHs and ABHs will be more significant. Therefore, this
can be served as a complementary method to distinguish PBHs from ABHs.
