  The screened modified gravity (SMG) is a unified theoretical framework, which
describes the scalar-tensor gravity with screening mechanism. Based on the
gravitational-wave (GW) waveform derived in our previous work
\citep{liu2018waveforms}, in this article we investigate the potential
constraints on SMG theory through the GW observation of the future space-borne
GW detectors, including LISA, TianQin and Taiji. We find that, for the EMRIs
consisting of a massive black hole and a neutron star, if the EMRIs are at
Virgo cluster, the GW signals can be detected by the detectors at quite high
significant level, and the screened parameter $\epsilon_{\rm NS}$ can be
constrained at about $\mathcal{O}(10^{-5})$, which is more than one order of
magnitude tighter than the potential constraint given by ground-based Einstein
telescope. However, for the EMRIs consisting of a massive black hole and a
white dwarf, it is more difficult to be detected than the previous case. For
the specific SMG models, including chameleon, symmetron and dilaton, we find
these constraints are complementary with that from Cassini experiment, but
weaker than those from lunar laser ranging observations and binary pulsars, due
to the strong gravitational potentials on the surface of neutron stars. By
analyzing the deviation of GW waveform in SMG from that in general relativity,
as anticipated, we find the dominant contribution of the SMG constraining comes
from the correction terms in the GW phases, rather than the extra polarization
modes or the correction terms in the GW amplitudes.
