Hydrodynamic simulations of gas clouds in the central hundred parsecs region of the Milky Way that is modeled with a three-dimensional bar potential are presented. Our simulations consider realistic gas cooling and heating, star formation, and supernova feedback. A ring of dense gas clouds forms as a result of $X_1-X_2$ orbit transfer, and our potential model results in a ring radius of ~200 pc, which coincides with the extraordinary reservoir of dense molecular clouds in the inner bulge, the Central Molecular Zone (CMZ). The gas clouds accumulated in the CMZ can reach high enough densities to form stars, and with an appropriate choice of simulation parameters, we successfully reproduce the observed gas mass and the star formation rate (SFR) in the CMZ, ${sim}2{ imes}10^7;M_{odot}$ and ${sim}0.1;M_{odot}/yr$. Star formation in our simulations takes place mostly in the outermost $X_2$ orbits, and the SFR per unit surface area outside the CMZ is much lower. These facts suggest that the inner Galactic bulge may harbor a mild version of the nuclear star-forming rings seen in some external disk galaxies. We also find that the stellar population resulting from sustained star formation in the CMZ would be enlogated perpendicularly to the main bar, and this "inner bar" can migrate the gas in the CMZ further down to the central parsecs region.