A new fuzzy based thresholding method for medical images especially cervical cytology images having blob and mosaic structures is proposed in this paper. Many existing thresholding algorithms may segment either blob or mosaic images but there aren't any single algorithm that can do both. In this paper, an input cervical cytology image is binarized, preprocessed and the pixel value with minimum Fuzzy Gaussian Index is identified as an optimal threshold value and used for segmentation. The proposed technique is tested on various cervical cytology images having blob or mosaic structures, compared with various existing algorithms and proved better than the existing algorithms.