The nonlinearity of photonic crystal fibers (PCFs) can be enhanced by simutaneously tapering the fiber and doping rare-earth ions (such as ${\mathrm{Yb}}^{3+}$ ) or chalcogenide in the core. The properties of the ${\mathrm{Yb}}^{3+}$ -doped and tapered PCF is numerically investigated by the beam propagation method. The results show that the difference of the optical field distribution between the doped and the pure silica PCF is not huge, and the mode field area of the doped PCF is only a little smaller than that of pure silica PCF. However, the nonlinearity of the doped PCF is enhanced dramatically by doping Yb ions in the core. Furthermore, the optimal boundary profile of the transverse structural parameters for maximal nonlinearity coefficient is acquired, and the boundary normalized pitch decreases exponentially with the boundary normalized hole size increasing. Finally, the longitudinal criterion for tapering is proposed, namely, that the normalized distance of the taper slope should be longer than $30\mu \mathrm{m}$ . All these results will provide references for enhancing the nonlinearity of PCFs.