<p>This paper presents a high-precision numerical method for solving backward parabolic equations defined in a bounded domain. Due to the inherent ill-posedness of these equations, direct numerical approaches are highly challenging. To overcome this, we apply the Fourier-truncated regularization method, which transforms the backward parabolic equation into an approximately well-posed integral equation. We then introduce the Legendre-Galerkin spectral method for numerically solving the resulting integral equation. Furthermore, we analyze both the error in the approximate analytical solution of the backward parabolic equation and the numerical error associated with the Legendre-Galerkin spectral method. Numerical experiments confirm the high-order accuracy of the proposed approach.</p>