We present the results of a directed search for continuous gravitational waves from unknown, isolated neutron stars in the Galactic center region, performed on two years of data from LIGO’s fifth science run from two LIGO detectors. The search uses a semicoherent approach, analyzing coherently 630 segments, each spanning 11.5 hours, and then incoherently combining the results of the single segments. It covers gravitational wave frequencies in a range from 78 to 496 Hz and a frequency-dependent range of first-order spindown values down to $-7.86\times {10}^{-8}\mathrm{Hz}/s$ at the highest frequency. No gravitational waves were detected. The 90% confidence upper limits on the gravitational wave amplitude of sources at the Galactic center are $\sim 3.35\times {10}^{-25}$ for frequencies near 150 Hz. These upper limits are the most constraining to date for a large-parameter-space search for continuous gravitational wave signals.