Parabolic equations on the unit sphere arise naturally in geophysics and oceanography when modeling physical quantities on large scales. In this paper, we consider the problem of finding the initial state for a backward parabolic problem on the sphere. This backward parabolic problem is ill-posed in the sense of Hadamard: the solutions may not exist, and even if they do, they may not depend continuously on the given observations. The backward problem for homogeneous parabolic equations was recently studied by Q.T.L. Gia, N.H. Tuan, and T. Tran. However, very few results exist for the backward problem of nonlinear parabolic equations on the sphere. In this paper, we do not focus on existence but on the stability of the solution, if it exists. By applying a regularization method and techniques involving spherical harmonics, we approximate the problem and obtain the convergence rate between the regularized and exact solutions.