This paper deals with Intuitionistic Fuzzy Linear Programming Problems (IFLPPs) using Symmetric Trapezoidal Intuitionistic Fuzzy Numbers (STIFNs) and the arithmetic operations defined on them. A special ranking function is presented in project environment to rank STIFN. An attempt has been made to solve the given IFLPP without converting them to crisp linear programming problems by using intuitionistic fuzzy simplex method and the algorithm is effective and reasonable as is evident from the results of a numerical example.