Medical imaging is one of the most daunting, challenging, and emerging research topics in image processing. Segmenting the glioma from the brain magnetic resonance images (MRI) is an important and demanding task, as it assists the medical experts for the disease diagnosis process. Recent research methods in image segmentation have highlighted the prospective of graph-based techniques for medical applications. As graph cut (GC) method is interactive in nature, it requires manual selection of the initial kernels for processing. The popularity of the GC method is limited by the occurrence of small cuts due to its shrinkage behavior leading to inaccurate extraction causing erroneous regions. This paper addresses the open research issue of shrinkage behavior by proposing the gradient based kernel selection (GBKS) GC method emphasizing on the directive inclination of the intensity scales. The proposed technique aids in the initialization of GC, removes the shrinkage problem, and locates the tumor in brain images without any human intervention. The performance results of the proposed GBKS GC method are evaluated on high-grade glioma and low-grade glioma MRI images and are analyzed and compared by using various measures. All the results present a remarkable improvement with GBKS GC technique over other existing techniques.