We use grid-based hydrodynamic simulations to study star formation in nuclear rings in barred galaxies. The gaseous medium is assumed to be infinitesimally thin, isothermal, and unmagnetized. To investigate various situations, we vary the total gas content in the bar regions and the bar growth time. We find that star formation rate (SFR) in a nuclear ring is determined by the mass inflow rate to the ring rather than the total gas mass in the ring. The SFR shows a strong primary burst and weak secondary bursts at early time, and declines to small values at late time. The primary burst is caused by the rapid gas infall to the ring due to the bar growth, with its duration and peak depending on the bar growth time. The secondary bursts result from re-infall of the ejected gas by star formation feedback of the primary burst. When the SFR is low, ages of young star clusters exhibit an azimuthal gradient along the ring since star formation takes place mostly near the contact points between the dust lanes and the nuclear ring. When the SFR is large, on the other hand, star formation is widely distributed throughout the whole length of the ring, with no apparent age gradient of star clusters. Regardless of SFR, star clusters have a positive radial age gradient, with younger clusters located closer to the ring, since the ring shrinks in size over time.