  In this article, we focus on a new scalar $\phi$ mediated scalar/vectorial
WIMPs (weakly interacting massive particles) with $\phi$'s mass slightly below
the WIMP mass. To explain the Galactic center 1 - 3 GeV gamma-ray excess, here
we consider the case that a WIMP pair predominantly annihilates into an
on-shell $\phi \phi$ pair with $\phi$ mainly decaying to $\tau \bar{\tau}$. The
masses of WIMPs are in a range about 14 - 22 GeV, and the annihilations of
WIMPs are phase space suppressed today. In this annihilation scheme, the
couplings of the $\phi$ - standard model (SM) particles are almost arbitrary
small, and the WIMP-nucleus spin-independent scattering can be tolerant by the
present dark matter (DM) direct detections. A scalar mediator-Higgs field
mixing is introduced, which is small and available. The lower limit on the
couplings of the $\phi$-SM particles set by the thermal equilibrium in the
early universe is derived, and this constraint is above the neutrino background
for scalar DM in direct detections. The WIMPs may be detectable at the upgraded
DM direct detection experiment in the next few years, and the exotic decay $h
\rightarrow \phi \phi$, the production of $\phi$ may be observable at future
high-luminosity $e^+ e^-$ collider.
