A number of models exist for estimating software development and duration. The most popular are COCOMO II, COSYSMO, and SLIM. Most of them use a line of codes as input data and do not give interval estimation results. In this article, a model for estimating software development effort and duration on the initiation project phase is proposed. The result which can be reasonably anticipated is based on the criteria outlined in Steven C. Mc-Connells research. The input data for the model, taken from the project charter, contains a description of high level requirements and risks. The input data for the model use fuzzy linguistic variable forms represented by Gaussian combination membership functions. Calculations are based on operations with fuzzy numbers. For the estimation of project duration, a modified Takagi-Sugeno (TSK) fuzzy inference model has been used. TSK models usually have a crisp input and output values. For the modified model, a method for calculating the degree to which fuzzy input belong to fuzzy sets via membership functions has been suggested. In addition, proposed a method for calculating fuzzy output of TSK model. The fuzzy output from the modified TSK model has been used for calculating the cumulative distribution function of the project duration. Finally, a comparison has been made between the proposed model and COCOMO II. It shows that the proposed model is more optimistic in effort estimation than COCOMO II.