This article is a continuation of the work done by W. Grecksch and P. E. Kloeden. In both articles the authors consider numerical schemes for a class of parabolic stochastic partial differential equations (SPDE) \(dU_t=\{AU_t + f(U_t)\}dt + g(U_t)dW_t\), with a strongly monotone linear operator \(A\) in the drift term and \(W\) being a standard scalar Wiener process. They use the eigenfunctions corresponding to the eigenvalues of \(A\) to obtain Galerkin approximations to this SPDE. The resulting equation is a finite-dimensional Itô stochastic ordinary differential equation (SODE). They then propose to use strong Taylor methods of order \(\gamma\) to solve this SODE. In the article by Grecksch and Kloeden, the authors use explicit strong Taylor methods and obtain an error bound for the combined truncation and global discretization error of the method. In a factor of this bound powers of some eigenvalue of \(A\) appear, which may be large for large dimensional systems. In this case very small time-steps are required to obtain a reasonable bound, which in turn may result in numerical instabilities. In the present article the authors propose to avoid this problem by using linear-implicit Taylor methods. They obtain an error bound for this method and, in particular, show that it does not contain the factor with powers of the eigenvalues.