Aims. The high-magnification microlensing event KMT-2021-BLG-1077 exhibits a subtle and complex anomaly pattern in the region around the peak. We analyze the lensing light curve of the event with the aim of revealing the nature of the anomaly. Methods. We test various models in combination with several interpretations: that the lens is a binary (2L1S), the source is a binary (1L2S), both the lens and source are binaries (2L2S), or the lens is a triple system (3L1S). We search for the best-fit models under the individual interpretations of the lens and source systems. Results. We find that the anomaly cannot be explained by the usual three-body (2L1S and 1L2S) models. The 2L2S model improves the fit compared to the three-body models, but it still leaves noticeable residuals. On the other hand, the 3L1S interpretation yields a model explaining all the major anomalous features in the lensing light curve. According to the 3L1S interpretation, the estimated mass ratios of the lens companions to the primary are ~1.56 × 10 −3 and ~1.75 × 10 −3 , which correspond to ~1.6 and ~1.8 times the Jupiter/Sun mass ratio, respectively, and therefore the lens is a multiplanetary system containing two giant planets. With the constraints of the event time-scale and angular Einstein radius, it is found that the host of the lens system is a low-mass star of mid-to-late M spectral type with amass of M h = 0.14 −0.07 +0.19 M Θ , and it hosts two gas giant planets with masses of M p1 = 0.22 −0.12 +0.31 M J and M p2 = 0.25 −0.13 +0.35 . The planets lie beyond the snow line of the host with projected separations of a ⊥,p1 = 1.26 −1.08 +1.41 AU and a ⊥,p2 = 0.93 −0.80 +1.05 AU. The planetary system resides in the Galactic bulge at a distance of D L = 8.24 −1.16 +1.02 kpc. The lens of the event is the fifth confirmed multiplanetary system detected by microlensing following OGLE-2006-BLG-109L, OGLE-2012-BLG-0026L, OGLE-2018-BLG-1011L, and OGLE-2019-BLG-0468L.