The generalized Gaussian distribution is useful in analyzing the data sets arising at places like Image processing, Signal processing, Speech recognition, Statistical Quality Control, Industrial experimentation, and Biological experiments. In this paper, a Left Truncated Generalized Gaussian distribution is introduced. The various distributional properties such as the distribution function, the four moments, skewness, kurtosis, hazard function, survival function are derived. The distribution of the rth order statistics, the median distribution also obtained. Some inferential aspects of the distribution are studied. An application of the suggested model is given with respect to the data on the length of fish in a catch.