A new model of an optical parametric amplifier is proposed based on a silicon-slab slotted photonic crystal waveguide (SPCW). The slot is considered to be filled with silicon nanocrystal material (SiNC/SiO2) having a high Kerr nonlinearity. The extreme optical confinement (spatial and temporal) of the SPCW has enhanced the optical nonlinearity, and thus, a high parametric gain is attained in a small length of the waveguide. Further, for analyses of pulse propagation, the coupled nonlinear Schrodinger’s equations have been modified to incorporate the enhancements in the linear and the nonlinear coefficients due to the slow-light effect. Simulations have been performed on both the high group index region and the low-dispersion regions of the guided band. The simulations on the high group index region, centered at ≈1584 nm, depict a 22.6 dB parametric gain and a 20.9 dB conversion efficiency at a waveguide length of 152 μm, with an effective pump power and peak input signal power of 700 mW and 0.25 Mw, respectively. The pulsating signal, with a pulse width of 5 ps, also experienced a negligible deterioration in its pulse shapes in this length of the SPCW. On the other hand, the simulations on the region of negligible dispersion, centered at 1530 nm, have produced an over 10 dB parametric gain and conversion efficiency through a long range of wavelengths, i.e., 1490–1568 nm, which covers half of the S-band and the complete C-band of the optical communication windows. The significant gain at a micrometer scale length of the waveguide is expected to advance the possibility of on-chip integration of a high-speed all-optical amplifier in photonic integrated circuits.