In this paper, a Stochastic Non-Homogeneous ARnoldi (SNHAR) method is proposed for the analysis of the on-chip power grid networks in the presence of process variations. In SNHAR method, the polynomial chaos based stochastic method is employed to handle the variations of power grids. Different from the existing StoEKS method which uses extended Krylov Subspace (EKS) method to compute the coefficients of the polynomial chaos, a computation-efficient and numerically stable Non-Homogeneous ARnoldi (NHAR) method is employed in SNHAR method to compute the coefficients of the polynomial chaos. Compared with EKS method, NHAR method has superior numerical stability and can achieve remarkably higher accuracy with even lower computational cost. As a result, SNHAR can capture the stochastic characteristics of the on-chip power grid networks with higher accuracy, but even lower computational cost than StoEKS.