We present K - band spectra of more than 110 M giants in Galactic bulge fields interior to - 4 degrees and as close as 0.2 degrees of the Galactic Center . From the equivalent widths of three features in these spectra , EW ( Na ) , EW ( Ca ) , and EW ( CO ) we calculate [ Fe/H ] for the stars with a calibration derived from globular clusters ( 23 ) . The mean [ Fe/H ] for each field is in good agreement with the results from Frogel et al . ( 8 ) based on the slope of the giant branch method . We find no evidence for a metallicity gradient along the minor or major axes of the inner bulge ( R < 0.6 kpc ) . A metallicity gradient along the minor axis , found earlier , arises when fields located at larger galactic radius are included . However , these more distant fields are located outside of the infrared bulge defined by the COBE/DIRBE observations . We compute the [ Fe/H ] distribution for the inner bulge and find a mean value of -0.21 dex with a full width dispersion of 0.30 dex , close to the values found for Baade ’ s Window ( BW ) by Sadler et al . ( 22 ) and to a theoretical prediction for a bulge formed by dissipative collapse ( 16 ) .