Due to the conventional look-up-table (LUT) using the static random access memory (SRAM) cell, field programmable gate arrays (FPGAs) almost reach the limitation in term of the density, speed, and configuration overhead. This paper proposes an improved memristor-based LUT (MLUT) circuit which is compatible with the mainstream LUT circuit in FPGA. Any arbitrary combined logic functions can be implemented in the MLUT through specific configurations. Then the MLUT shows superior advantages over the conventional LUT such as smaller area overhead and fewer data transmission. As a case study, a one-bit full adder is simulated to verify that the design is of practice in PSPICE. Moreover, the adder can be cascaded into multibit full adder demonstrating competitiveness against the conventional configurable logic block in FPGA technology. MLUT can be a candidate to replace the conventional SRAM-based LUT and further improves the performance of FPGAs.