Local field potentials (LFPs) have been demonstrated to be an important measurement to study the activity of a local population of neurons. The response tunings of LFPs have been mostly reported as weaker and broader than spike tunings. Therefore, selecting optimized tuning methods is essential for appropriately evaluating the LFP responses and comparing them with neighboring spiking activity. In this paper, new models for tuning of the contrast response functions (CRFs) are proposed. To this end, luminance contrast-evoked LFP responses recorded in primate primary visual cortex (V1) are first analyzed. Then, supersaturating CRFs are distinguished from linear and saturating CRFs by using monotonicity index (MI). The supersaturated recording data are then identified through static identification methods including multilayer perceptron (MLP) neural network, radial basis function (RBF) neural network, fuzzy model, neuro-fuzzy model, and the local linear model tree (LOLIMOT) algorithm. Our results demonstrate that the MLP neural network, compared to traditional and modified hyperbolic Naka-Rushton functions, exhibits superior performance in tuning the local field potential responses to luminance contrast stimuli, resulting in successful tuning of a significantly higher number of neural recordings of all three types. These results suggest that the MLP neural network model can be used as a novel approach to measure a better fitted contrast sensitivity tuning curve of a population of neurons than other currently used models.