Spectral mixture analysis (SMA) is an effective means of finding a unique spectral signature of constituents called endmembers and approximating their proportion of presence (abundance fractions). In the literature of SMA, the challenging task of endmember extraction from the hyperspectral imagery is approached by different methods. The majority of the endmember extraction algorithms are developed based on the convex geometry of the dataset perhaps due to low computation. But the performance of these convex geometry-based algorithms is degraded in the high-level noise scenario. To make the noise-robust algorithm, we propose an algorithm by introducing K-medoids with convex geometry. The proposed algorithm uses the K-medoids clustering approach in the removal of extra convex points, which leads to improving the endmember extraction efficacy. The proposed algorithm is tested by introducing white Gaussian noise under different signal-to-noise ratio conditions in the synthetic dataset, especially for high-level noise. Our experimental results show that the proposed one improves the endmember extraction efficiency in the high-level noise condition. The proposed algorithm is also tested on the real datasets of Cuprite and Mangalore. The proposed algorithm outperforms others on the real benchmark datasets as well.