  Using a density dependent quark mass (QMDD) model for strange quark matter,
we investigate the effects of non-Newtonian gravity on the properties of
strange stars and constrain the parameters of the QMDD model by employing the
mass of PSR J0740+6620 and the tidal deformability of GW170817. We find that
for QMDD model these mass and tidal deformability observations would rule out
the existenceof str ange stars if non-Newtonian gravity effects are ignored.
For the current quark masses of $m_{u0}=2.16$ MeV, $m_{d0}=4.67$ MeV, and
$m_{s0}=93$ MeV, we find that a strange star can exist for values of the
non-Newtonian gravity parameter $g^{2}/\mu^{2}$ in the range of 4.58
GeV$^{-2}\leq g^{2}/\mu^{2}\leq$ 9.32 GeV$^{-2}$, and that the parameters $D$
and $C$ of the QMDD modelare restricted to 158.3 MeV$\leq D^{1/2}\leq$ 181.2
MeV and $-0.65\leq C \leq -0.12$. It is found that the largest possible maximum
mass of a strange star obtained with the QMDD model is $2.42 \, M_{\odot}$, and
that the secondary componentof GW190814 with a mass of 2.59_{-0.09}^{+0.08}\,
M_{\dot} could not be a static strange star. We also find that forthe mass and
radius of PSR J0030+0451 given by Riley et al. through the analysis of
observational data of NICER, there exists a very tiny allowed parameter space
for which strange stars computed for the QMDD model agree with the observations
of PSR J0740+6620, GW17 0817 and PSR J0030+0451 simultaneously. However, for
the mass and radius given by Miller et al., no such parameter space exist.
