This paper presents the stability analysis of voltage source inverters (VSIs) in the presence of asymmetrical weak grids. Large grid impedances associated with weak grids can make grid-connected VSIs unstable. State-of-the-art research on the stability in weak grids focuses solely on symmetrical grid impedances, with little attention paid to the asymmetrical grid impedance case. The stability analysis of VSIs in asymmetrical weak grids is studied in this paper based on a developed state-space model of a grid-connected VSI considering asymmetrical grid impedances. Root locus studies of the eigenvalues of the model show that an asymmetrical increase in the grid impedance could result in instability for an otherwise stable system in the balanced case. The results are verified through simulations and experiments for a three-phase 208V grid-connected hardware setup for both symmetrical and asymmetrical weak grid cases.