The invention provides seed and plants of the tomato line designated FIR 128-1018. The invention thus relates to the plants, seeds and tissue cultures of tomato line FIR 128-1018, and to methods for producing a tomato plant produced by crossing a plant of tomato line FIR 128-1018 with itself or with another tomato plant, such as a plant of another line. The invention further relates to seeds and plants produced by such crossing. The invention further relates to parts of a plant of tomato line FIR 128-1018, including the fruit and gametes of such plants.