QCA is regarded as one of the new technologies to replace CMOS due to its advantages of short delay time, low power consumption, and small footprint. In response to the high power consumption, capacitance parasitic, and crosstalk issues caused by the decreasing size of CMOS devices, this paper constructs a recursive box filter using QCA technology for the first time. Among them, a new QCA full adder has been proposed, which reduces the circuit area by 55% compared to the proposed QCA full adder. 56. 7% fewer cells were used. Quantum costs have also been reduced by more than 10%. Based on this, an efficient RCA and an efficient CSA were designed to form the addition unit of the box filter. The box filter constructed based on this saves 32. 6% of hardware resources compared to general QCA box filters. Reduce circuit running time by 20%. Reduced power consumption by 48. 7%. And simulated using QCA Designer, the results show that this design can completely replace the traditional box filter function, and significantly reduce efficiency, power consumption, circuit area, and resource occupation.