  We study the impact of Ly$\alpha$ radiation feedback on globular cluster (GC)
formation. In this Letter, we analytically derive the relation between star
formation efficiency (SFE) and metallicity in spherical clouds with the
Ly$\alpha$ radiation feedback. Our models show that the SFE becomes small as
the metallicity decreases. In metal-poor gas clouds, Ly$\alpha$ photons are
trapped for a long time and exert strong radiation force to the gas, resulting
in the suppression of star formation. We find that bound star-clusters (SFE
$\gtrsim$ 0.5) form only for the metallicity higher than $\sim
10^{-2.5}~Z_{\odot}$ in the case with the initial cloud mass $10^5~{\rm
M}_\odot$ and the radius 5 pc. Our models successfully reproduce the lower
bound of observed metallicity of GCs. Thus, we suggest that the Ly$\alpha$
radiation feedback can be essential in understanding the formation of GCs.
