The plane curve approach which was proposed by Boukharouba et. al. is a multi-threshold selection method through searching peak-valley based on histogram cumulative distribution function. However the method is required to select parameters to compose plane curve, and the shape of plane curve is affected according to parameters. Therefore detection of peak-valley is effected by parameters. In this paper, we propose an entropy maximizing-based method to select optimal plane curve parameters, and propose a multi-thresholding method based on the selected parameters. The effectiveness of the proposed method is demonstrated by multi-thresholding experiments on various images and comparison with other conventional thresholding methods based on histogram.