We determined the ages, kinematic parameters, and Galactic orbital parameters of six metal-poor (-2.4 < [Fe/H] < -1.0 dex), F-type, high-proper-motion (HPM) stars to investigate their HPM nature and origin. For the kinematical procedure, the astrometric data from the Gaia DR2 were used. High-resolution ELODIE spectra of the six dwarfs were also used to obtain accurate [Fe/H] abundances and up-to-date [alpha/Fe] abundances. The calculations for stellar ages were based on Bayesian statistics, with the computed ages falling in the range 9.5-10.1 Gyr. On the basis of the metallicities and ages, six HMP stars are either members of the halo (HD 6755, HD 84937, BD +42 3607) or members of the low-metallicity tail of the thick disk (HD 3567, HD 194598, HD 201891). However, Galactic orbital parameters suggest thin disk (HD 84937, HD 194598), thick disk (HD 3567, HD 201891), and halo (HD 6755, BD +42 3607) populations. The dynamical analysis was also performed for the escape scenario from the candidate GCs. The tidal disruption of a dwarf galaxy was also considered as an alternative origin. HD 6755, HD 194598, and HD 3567, with their retrograde orbital motions, are likely candidate stars for a tidally disrupted dwarf galaxy origin. However, the relationship of HD 194598 with NGC 6284 presents an interesting case. Its encounter velocity is low (16 28 km s(-1)), and their ages and metallicities are very nearly consistent with each other at the 1 sigma level. The rest of the HPM sample stars have a 4%-18% probability of encountering with selected GCs for 1.5 tidal radii. This indicates that a globular cluster origin for the program stars is unlikely.