Although parallel imaging is a routine technique in clinical magnetic resonance imaging (MRI), estimating coil sensitivities remains a constant challenge to accelerated MRI. Recent coil estimation methods are computationally expensive, requiring external libraries to compute the singular-value decomposition (SVD) of a large matrix. Moreover, phase variations can appear in the final complex-valued coil sensitivity profiles. For instance, phase singularity is frequently observed in contrast-enhanced MRI. In this study, a robust generalized eigenvalue problem (GEP) approach is proposed to address the phase variations (also known as phase flipping or phase singularity) in complex-valued coil sensitivity of parallel MRI. Based on the inexact inverse iteration method in the outer loop and the conjugate gradient method in the inner loop, the low-cost inexact inverse iteration improves the homogeneity of the coil sensitivity without phase variations of the existing method. We performed repeated simulation studies. Results of 2D and 3D computational simulations are demonstrated, and the potential use of the method is also discussed.