We demonstrate dynamic parametric optical dispersion compensation in dynamic optical path networks (DOPNs). A fully automatic parametric tunable dispersion compensator (P-TDC) based on four-wave mixing process is developed with a fast tunable distributed amplification chirped sampled grating distributed reflector laser, a field-programmable gate array (FPGA) pump controller, and a fast dispersion monitor based on spectral shearing interferometer. The dispersion monitor detects a change in the dispersion of a path, and the monitoring signal is fed forward to the FPGA controller. The fast tunable laser sets its wavelength accordingly for the dispersion compensation through parametric process. A response time of <17 ms is demonstrated in a testbed of DOPN. The autonomous P-TDC has a potential response of submillisecond.