The anisotropy-based/H-infinity suboptimal filtering problem for linear discrete time-invariant system with nonzero-mean stochastic input is considered. The filtering goal is to minimize the anisotropic norm of a given system and to satisfy the H-infinity norm restriction. The input disturbance is supposed to be a sequence of the Gaussian noncentered random vectors with unknown distribution parameters and with bounded mean anisotropy. The original problem is reduced to the optimization problem with convex restrictions. The solution is based on the sufficient condition for boundedness of the anisotropic norm.