  We construct a generic model of Majorana fermionic dark matter (DM). Starting
with two Weyl spinor multiplets $\eta_{1,2}\sim (I,\mp Y)$ coupled to the
Standard Model (SM) Higgs, six additional Weyl spinor multiplets with $(I\pm
1/2, \pm(Y\pm 1/2))$ are needed in general. It has 13 parameters in total, five
mass parameters and eight Yukawa couplings. The DM sector of the minimal
supersymmetric standard model (MSSM) is a special case of the model with
$(I,Y)=(1/2,1/2)$. Therefore, this model can be viewed as an extension of the
neutralino DM sector. We consider three typical cases: the neutralino-like, the
reduced and the extended cases. For each case, we survey the DM mass $m_\chi$
in the range of $(1,2500)$ GeV by random sampling from the model parameter
space and study the constraints from the observed DM relic density, the direct
search of LUX, XENON100 and PICO experiments, and the indirect search of
Fermi-LAT data. We investigate the interplay of these constraints and the
differences among these cases. It is found that the direct detection of
spin-independent DM scattering off nuclei and the indirect detection of DM
annihilation to $W^+W^-$ channel are more sensitive to the DM searches in the
near future. The allowed mass for finding $\tilde H$-, $\tilde B$-, $\tilde W$-
and non neutralino-like DM particles and the predictions on $\langle\sigma
(\chi{\chi}\rightarrow ZZ, ZH, t{\bar t}) v\rangle$ in the indirect search are
given.
