Spot centroiding is the key technique used in optical precise tracking and measurement, and its precision and speed affect those of optical tracking systems directly. In the applications, image pre-processing methods, which suppress the noise effectively at the expense of logic resources, are combined with the conventional mass of gravity to improve the reliability of spot centroid calculation. In order to realize real-time spot detection with resources limited, a high-speed spot centroid calculation method without multipliers is proposed. Instead of multiplications, it uses additions in recursive way to compute all low order moments needed by spot centroding. Compared with the architecture of the conventional mass of gravity method, our method needs only five accumulators, thus the resource cost is much lower than that of multipler-based spot detection. Moreover, the operating frequency of the hardware implementation of our method is up to 515 MHz with parallel and pipeline architecture. Experimental results indicate that when implemented in Field Programmable Gate Array at 100 MHz, our design can determine the spot centroid accurately with latency no more than 0.35 us at the cost of 214 slices, which is only half of resource consumption of the conventional method.