We use grid-based hydrodynamic simulations to study star formation history in nuclear rings of barred-spiral galaxies. In our previous study, we concentrated on bar-only galaxies without spirals, finding that the star formation rate (SFR) in a nuclear ring exhibits a strong primary burst at early time before decreasing to below 1 $M_{odot}/yr$ at late time. The rapid decline is caused by the paucity of the gas in the bar region, due to early massive gas inflows to the nuclear ring. Since star formation in nuclear rings is observed to be sustained for about 1-2 Gyr, this requires mechanisms to supply the gas to the bar regions. In this work, we study the effect of spiral arms on the radial gas inflows and related star formation in the nuclear rings. We show that spiral arms are efficient to remove angular momentum of the gas to cause significant gas inflows to the bar region, provided the patten speed of the arms is much smaller than that of the bar. The inflowing gas is added to a nuclear ring, making the ring SFR episodic over a long period of time. The time interval of multiple bursts of star formation is a few tens to hundred million years, with the mean peak SFR of ${sim}5M_{odot}/yr$, consistent with observations of M100.