This paper presents a novel low-complexity soft demapping algorithm for two-dimensional non-uniform spaced constellations (2D-NUCs) and massive order one-dimensional NUCs (1D-NUCs). NUCs have been implemented in a wide range of new broadcasting systems to approach the Shannon limit further, such as DVB-NGH, ATSC 3.0 and NGB-W. However, the soft demapping complexity is extreme due to the substantial distance calculations. In the proposed scheme, the demapping process is classified into four cases based on different quadrants. To deal with the complexity problem, four groups of reduced subsets in terms of the quadrant for each bit are separately calculated and stored in advance. Analysis and simulation prove that the proposed demapper only introduces a small penalty under 0.02dB with respect to Max-Log-MAP demapper, whereas a significant complexity reduction ranging from 68.75% to 88.54% is obtained.