Dark solitons, localized nonlinear waves with center notch standing on a stable uniform background, own rich formation and dynamics for physics and applications in diverse fields, and have thus recently attracted many theoretical and experimental studies. Transverse modulational instability is an impeditive factor for dark solitons in multidimensional space, to stabilize them various methods have been proposed. We here take use of a purely nonlinear strategy by introducing quasi-one-dimensional Gaussian like trap, and its combination with the external linear harmonic trap, in the framework of the (2 + 1)-dimensional Gross-Pitaveski/nonlinear Schrödinger equation, to realize the stabilization mechanism of dark-soliton stripes. Variational approximation analytical method, linear-stability analysis and direct perturbed numerical simulations are adopted to carry out the study, and agreement is reached. We demonstrate that the dark-soliton stripes can be stabilized completely, and the associated modulational instability wave number band is reduced greatly. Particularly, in the case of linear harmonic trap, the nucleation of dark solitons, subjected to snaking instability, can be overcome by the nonlinear trap with both defocusing and focusing strengths. The predicted results may be realized in Bose-Einstein condensates and nonlinear optics. © 2022 Elsevier Ltd