A complete solution of the ground-state problem for the Ising model on an anisotropic triangular lattice with the nearest-neighbor interactions in a magnetic field is presented. It is shown that this problem can be reduced to the ground-state problem for an infinite chain with the interactions up to the second neighbors. In addition to the known ground-state structures (which correspond to full-dimensional regions in the parameter space of the model), new structures are found (at the boundaries of these regions), in particular, zigzagging stripes similar to those observed experimentally in colloidal monolayers. Though the number of parameters is relatively large (four), all the ground-state structures of the model are constructed and analyzed and therefore the paper can be considered as an example of a complete solution of a ground-state problem for classical spin or lattice-gas models. The paper can also help to verify the correctness of some results obtained previously by other authors and concerning the ground states of the model under consideration.