Sudoku, an NP-complete-based mathematical puzzle, has different levels of difficulty. There are several techniques to solve this interesting mathematical conundrum. Our effort anticipated a neighbourhood-based mutation approach of the Genetic Algorithm to solve Sudoku instances. In this paper, the fixed two-point crossover along with neighbourhood-based mutation is implemented. For mutation, a neighbour checking concept is incorporated to get rid of unwanted swaps. The newness of our proposed method is that considering less population Sudoku instances can be solved with a greater success rate for easy, medium, and hard difficulty level puzzles. © 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.