Traveling Salesman Problem (TSP) is an NP-hard Problem, which has so many different real life applications. Precedence Constraint TSP (PCTSP) is one specific type of TSP in which precedence is given to some cities. PCTSP also has numerous applications. Genetic Algorithms  are robust and probabilistic search algorithms based on the mechanics of natural selection and survival of fittest. This paper basically presents the idea to solve PCTSP using Genetic Algorithm efficiently & faster. Moreover this paper shows best suitable probability of Crossover & Mutation operator for small population size and less number of generations for PCTSP, which is required for faster response.