We investigate the star formation history of the central regions of four Luminous Compact Blue Galaxies ( LCBGs ) at intermediate redshift using evolutionary population synthesis techniques . LCBGs are blue ( \bv \leq 0.6 ) , compact ( \mu _ { B } \leq 21.0 mag arcsec ^ { -2 } ) galaxies with absolute magnitudes M _ { B } brighter than -17.5 . The LCBGs analyzed here are located at 0.436 \leq z \leq 0.525 . They are among the most luminous ( M _ { B } < -20.5 ) , blue ( \bv \leq 0.4 ) and high surface brightness ( \mu _ { B } \leq 19.0 mag arcsec ^ { -2 } ) of this population . The observational data used were obtained with the HST/STIS spectrograph , the HST/WF/PC-2 camera and the HST/NICMOS first camera . We have disentangled the stellar generations found in the central regions of the observed targets using a very simple model . This is one of the first times this is done for compact galaxies at this redshift using Hubble Space Telescope data , and it provides a comparison bench for the future work on this kind of galaxies using instruments with adaptive optics in 10-m class telescopes . We find evidence for multiple stellar populations . One of them is identified as the ionizing population , and the other one corresponds to the underlying stellar generation . The estimated masses of the inferred stellar populations are compatible with the dynamical masses , which are typically 2–10 \times 10 ^ { 9 } M _ { \odot } . Our models also indicate that the first episodes of star formation the presented LCBGs underwent happened between 5 and 7 Gyr ago . We compare the stellar populations found in LCBGs with the stellar populations present in bright , local H ii galaxies , nearby spheroidal systems and Blue Compact Dwarf Galaxies . It turns out that the underlying stellar populations of LCBGs are similar yet bluer to those of local H II galaxies . It is also the case that the passive color evolution of the LCBGs could convert them into local Spheroidal galaxies if no further episode of star formation takes place . Our results help to impose constraints on evolutionary scenarios for the population of LCBGs found commonly at intermediate redshifts .