We present the results of deep imaging of the field of GRB 050904 with Suprime-Cam on the Subaru 8.2m telescope. We have obtained a narrow-band (130 A) image centered at 9200 A (NB921) and an i-band image with total integration times of 56700 and 24060 s, respectively. The host galaxy was not detected within 1 of the afterglow position. An object was found at 1.5 NE from the position of the afterglow, but clear detection of this object in the i-band image rules out its association with the burst. We obtained a limit of > 26.4 AB magnitude (2 diameter, 3 sigma) in the NB921 image for the host galaxy, corresponding to a flux of 6.0 x 10^{28} erg/s/Hz at rest 1500 A assuming a flat spectrum of the host galaxy. The star formation rate should be less than 7.5 (M_{solar}/yr) based on the conversion rate by Madau et al (1998). This upper limit for the host of GRB 050904 is consistent with the star formation rate of other gamma-ray burst host galaxies around redshift of 2 or less.
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