In this paper, we systematically study the (1+1)-dimensional spatial optical solitons in nematic liquid crystals with negative dielectric anisotropy. Firstly, with the perturbation method, we obtain a (1+1)-dimensional soliton solution in the second approximation.Numerical simulations confirm the analytical soliton solution in the strongly nonlocal case, the critical power of a strongly nonlocal solition is directly proportional to wm2/w3, where wm is a characteristic length of the material response, and w is the soliton width. Secondly, the soliton solutions in nematic liquid crystal with negative dielectric anisotropy are obtained by numerical computation. It is found that the bright solitons exist only when the degree of nonlocality is above a critical value. The analytical solutions in the second approximation accord with the numerical ones very well even under the general degree of nonlocality. Finally, to investigate the stability, we conduct the linear stability analysis, and find that all the solitons are stable, which is also confirmed by the numerical simulations.