Blowoff limits are essential in establishing the combustor operating envelope. Hence, there is a great demand for practical aero-engines to extend the blowoff limits further. In this work, the behavior of non-premixed swirling flames under fuel flow rate oscillations was investigated experimentally close to its blowoff limits. The methane flame was stabilized on the axisymmetric bluff body and confined in a square quartz enclosure. External acoustic forcing at 400 Hz was applied to the fuel flow to induce a fuel mass flow rate fluctuation (FMFRF) with varying amplitudes. A high-speed burst-mode laser and cameras ran at 20 kHz for OH*-chemiluminescence (CL), CH2O-, and SO2-PLIF measurements, offering the visualization of the two-dimensional flame structure and heat release distribution, temporally and spatially. The results show that the effect of FMFRF is predominantly along the central axis without altering the time-averaged flame structure and blowoff transient. However, the blowoff limits are extended due to the enhanced temperature and longer residence time induced by FMFRF. This work allows us to explore the mechanism of flame instability further.