The disclosure provides a dispersion management method and apparatus based on non-periodic spectral phase jumps. Precise dispersion is provided by virtue of non-periodic spectral phase jumps, the dispersion can be tuned freely with engineering of the phase jump. A device based on non-periodic spectral phase jump also has a wide working bandwidth and could promote the development of ultrafast optics. The method includes: spatially separating a light pulse with different frequency components, and meanwhile, making the light pulse with the different frequency components propagate in parallel; enabling the light pulse with the different frequency components and propagating in parallel to be incident on a non-periodic phase jump device to obtain non-periodic spectral phase jumps, forming a phase grating effect to obtain two ±1-order diffracted pulses having opposite group delays, and introducing frequency dependent relative delay for the different spectral components in the two diffracted pulses.