In this paper, we propose a high-density and fast-configuration non-volatile look-up table (NVLUT) based on a NAND-like spintronic memory (NAND-SPIN) by exploiting the interplay of spin transfer torque (STT) and spin orbit torque (SOT) effects. The proposed NVLUT utilizes a shared random-access module to realize both configuration and readout operations. The simulation results show that our proposed design achieves over 25.8%, 29.2% and 54% improvement in terms of area overhead, reconfiguration delay and sensing delay, respectively, in comparison with state-of-the-art counterparts.