In deregulated power markets, it is of high interest to have a mathematical representation of the LMP-Load curve for the purpose of various analytical studies such as probabilistic LMP analysis. However, LMP versus Load curve may present various linear and nonlinear patterns, and appears challenging to develop a simple and unified form of mathematical model to capture those patterns observed in the LMP-Load curve. Studies have shown that the LMP-Load curve presents change of patterns at Critical Load Levels (CLLs) where step changes of LMP occur. By utilizing the concept of CLLs, this paper proposes a method to divide a LMP-Load curve into segments, and employ linear curve-fitting to obtain a piece-wise linear model to represent the actual LMP-Load curve. Through accurately identified break points of the curve, the proposed method can very closely approximate the actual curve, which traditional curve fitting methods would fail to do. The method has been tested on a revised IEEE 118-bus system. The resulting piece-wise linear model has been verified to be an exceptionally accurate model to represent the actual LMP-Load curve. Various patterns of the curve have been captured and closely represented by the piece-wise linear approximation model.