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 semi-coherent 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 } \text { Hz } / \text { s } at the highest frequency . No gravitational waves were detected . Placing 90 % confidence upper limits on the gravitational wave amplitude of sources at the Galactic Center , we reach \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 .