  We systematically investigate the p-wave superfluidity of a Rydberg-dressed
Fermi gas, where the soft-core effective interaction is of finite radius
$R_{c}$ due to blockade effects. After solving the BCS gap equation and
comparing the free energy, we obtain the quantum phase diagram, which is
composed of three different phases: polar ($p_{z}$), axial ($p_{x}+ip_{y}$),
and axi-planar ($p_{x}+i\beta_{p}p_{y}$) phases. The tri-critical point locates
around $R_{c}k_{F}\sim1$, where $k_{F}$ is the Fermi wave vector. We further
derive the Ginzburg-Landau theory to explain the phase diagram, and estimate
the transition temperature to be about 0.1$E_{F}$ in the current experimental
regime of $^{6}$Li. Our work paves the way for future studies on p-wave
superfluids and related quantum phase transitions in ultracold atoms.
