We systematically investigate the topological superfluidity of a Rydberg-dressed Fermi gas, where the soft-core effective interaction is of finite radius
Rc due to the blockade effect. We calculate the quantum phase diagram within the mean-field approximation and find three distinct phases: polar
(pz), axial
(px+ipy), and axiplanar $({p}_{x}+i{\ensuremath{\beta}}_{p}{p}_{y})$ phases. The tricritical point is around ${R}_{c}{k}_{F}\ensuremath{\sim}1$, where
kF 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
0.1EF in the current experimental regime of
6Li. Our work paves the way for future studies on exotic topological superfluids and related quantum phase transitions.