This paper presents the sixth extension to the Very Long Baseline Array (VLBA) Calibrator Survey. It contains the positions and maps of 264 sources of which 169 were not previously observed with very long baseline interferometry (VLBI). This survey, based on two 24 hour VLBA observing sessions, was focused on 1) improving positions of 95 sources from previous VLBA Calibrator surveys that were observed either with very large a priori position errors or were observed not long enough to get reliable positions and 2) observing the remaining new flat-spectrum sources with predicted correlated flux density in the range 100--200 mJy that were not observed in previous surveys. Source positions were derived from astrometric analysis of group delays determined at the 2.3 and 8.6 GHz frequency bands using the Calc/Solve software package. The VCS6 catalogue of source positions, plots of correlated flux density versus projected baseline length, contour plots and fits files of naturally weighted CLEAN images, as well as calibrated visibility function files are available on the Web at http://vlbi.gsfc.nasa.gov/vcs6.