A prism compressor can compensate dispersion of femtosecond light pulses travelling in air for laser ranging. An accurate expression of the group delay dispersion (GDD) of a prism compressor at arbitrary incident angle and at arbitrary incident point is obtained, which is of benefit to finely compensating dispersion of femtosecond pulses. Influences of several parameters on group delay dispersion are analyzed for the active compensation of dispersion of femtosecond pulses. These expressions are convenient to applications of intra- and extra-cavity dispersion compensation of ultra-short laser pulses, as well as fine compensation of satellite laser ranging and laser altimetry.