A Sudoku puzzle of rank n, for some positive integer n, is defined as a grid of size \(n^2 \times n^2\) partitioned into \(n \times n\) distinct blocks and the task is to fill each cell of the grid so that each row, each column and each block contain the integers 1 through \(n^2\) exactly once. Its solution is known as a Sudoku square. The problem of completing partial Sudoku squares is NP-complete. Therefore, many researchers have used various heuristic approaches to find the complete solution of a given Sudoku puzzle. In this work, an improved genetic algorithm is given for solving these Sudoku puzzles. This genetic algorithm uses new knowledge based multiple inversion operator and a neighborhood swapping operator to solve these puzzles. The performance of the algorithm is shown for 50 puzzles of rank 3 (of size \(9 \times 9\) ) of varying difficulty levels. The experimental results indicate that the new algorithm produces competitive results with respect to other evolutionary algorithms used to solve these puzzles.