Finite-time performance of genetic algorithm with elitist operator in finite solution space is studied, and the relationship between evolution generation and the quality of the solution found best so far is analyzed. The estimating formulations of the expectation value as well as upper bound and lower bound for the evolution generation earliest achieving specific performance are provided. Finite-time performance of genetic algorithm with elitist operator in finite solution space is studied, and the relationship between evolution generation and the quality of the solution found best so far is analyzed. The estimating formulations of the expectation value as well as upper bound and lower bound for the evolution generation earliest achieving specific performance are provided.