We present two semi-detached binaries with extremely low mass-ratio (<0.1). The total eclipse feature on the light curves greatly improves the reliability of the binary light analysis results. Combining the photometric and spectral data, both the relative and the absolute parameters were obtained based on two methods. The masses and radii areM(1) = 1.21 0.45M,M-2 = 0.116 0.044M,R-1 = 1.89 0.25R, andR(2) = 0.76 0.1Rfor KIC 2719436, andM(1) = 1.58 0.49M,M-2 = 0.153 0.051M,R-1 = 1.9 0.28R, andR(2) = 5.14 0.79Rfor KIC 4245897. The binaries with extremely low mass-ratios provide a laboratory to study the binary outcomes as well as the extremely low-mass stars with complete physical properties. KIC 2719436 is an abnormal semi-detached binary system for its primary radius is much larger than that of the evolved secondary star who fills its own Roche Lobe. Excessive mass transfer leads to this situation on account of the effective angular momentum loss probably by the magnetic braking. KIC 2719436 is possible the closest target to the end as a single star that predicted by the TRO theory.