Quantum-dot Cellular Automata (QCA) has become one of the promising studies for nano-scale computing. QCA is one of the candidate technologies to be replaced with CMOS technology. QCA technology not only reduces power consumption and delay but also increases operating frequency and speed. The arithmetic logic unit is the essential component in a processor that performs arithmetic and logical operations. This paper presents a novel 5 × 5 reversible logic gate called the NRRG (Norouzi_Rasouli Reversible Gate) which can be used as the basic building block of 4:1 and 8:1 reversible multiplexers. Then, we have designed a RALU (reversible arithmetic and logic unit) using this gate. Our design can perform 20 operations such as AND, NAND, OR, XOR, XNOR, COPY, addition, and increment. The proposed QCA RALU requires 0.44 μm2 area, 480 QCA cells, and 10 clock phases. The proposed design needs less cell count, delay, and cost of QCA compared to previous works. The structure is implemented without any rotated cells and only uses one layer which improves the manufacturability of the design. The architectures are designed and simulated using QCA Designer 2.0.3.