Rotating radio transients (RRATs) are neutron stars that emit sporadic radio bursts. We detected 1955 single pulses from RRAT J1913+1330 using the 19 beam receiver of the Five-hundred-meter Aperture Spherical radio Telescope. These pulses were detected in 19 distinct clusters, with 49.4% of them occurring with a waiting time of one rotation period. The energy distribution of these individual pulses exhibited a wide range, spanning 3 orders of magnitude, reminiscent of repeating fast radio bursts (FRBs). Furthermore, we observed abrupt variations in pulse profile, width, peak flux, and fluence between adjacent sequential pulses. These findings suggest that this RRAT could be interpreted as a pulsar with extreme pulse-to-pulse modulation. The presence of sequential pulse trains during active phases, along with significant pulse variations in profile, fluence, flux, and width, should be intrinsic to a subset of RRATs. Our results indicate that J1913+1330 represents a peculiar source that shares certain properties with populations of nulling pulsars, giant pulses, and FRBs from different perspectives. The dramatic pulse-to-pulse variation observed in J1913+1330 could be attributed to unstable pair creation above the polar cap region and the variation of the site where streaming pairs emit coherently. Exploring a larger sample of RRATs exhibiting similar properties to J1913+1330 has the potential to significantly advance our understanding of pulsars, RRATs, and FRBs.