A novel photonic crystal fiber featured by concentric cores is proposed to induce dispersion controllability by photosensitivity. Chromatic dispersion can be changed from $-1827$ to $72\mathrm{ps}∕\mathrm{nm}∕\mathrm{km}$ with refractive index modulation of $4\times {10}^{-4}$ produced in Ge-doped regions in the fiber. Effective mode area of inner mode is as small as $6.4\mathrm{\mu }{\mathrm{m}}^2$ . The proposed fiber enables to achieve quasi-phase-matched nonlinear parametric interaction in a single piece of photonic crystal fiber, by periodically alternating dispersion and compensating for phase mismatching caused by the dispersion.