Quantum-dot Cellular Automata (QCA) is one of the new nanoscale technologies which proposed for future circuits. This technology has been remarkable due to its faster speed, lower size and reduction in power consumption compared to CMOS technology. Many circuits have been implemented in this technology including shift registers, they are one of the most important digital circuits for many applications. With the development of QCA technology, it is important to provide testing methods for testing these circuits.4-Bit serial shift registers designed in previous research were not capable of testing their output. In this paper, MUXED-D scan cell concept helps to detect the errors before fabrication and reduce time and cost. The MUXED-D scan consists of a D flip-flop and a 2 to 1 multiplexer. Compared to the latest scan cell, we have seen a 25 % decrease in occupied area and 15.62 % decrease in the number of cells and latency from 1 to 0.75 clock cycle. In general, this scan cell circuit is made of 27 cells with an area of 0.03 µm2 and a latency of 3 clock cycles. The proposed shift register includes four scan cells with two inputs which includes main and test signals. In fact, the number of cells used for the last 4-bit serial testable shift register in this design is 324, 0.39µm2 occupied area and the corresponding delay is 6.75 clock cycles. In order to verify this performance, QCA simulator is used.