Over the last three decades, a great deal of research has been focused on solving the job-shop scheduling problem (JSSP). Researchers have emerged with a wide variety of approaches to solve this stubborn problem. Recently much effort has been concentrated on evolutionary techniques to search for the near-optimal solutions optimizing multiple criteria simultaneously. The choice of crossover operator is very important in the aspect of genetic algorithms (GA), and consequently a wide range of crossover operators have been proposed for JSSP. Most of them represent a solution by a chromosome containing the sequence of all the operations and decode the chromosome to a real schedule from the first gene to the last gene. However, these methods introduce high redundancy at the tail of the chromosome. In this paper, we address this problem in case of precedence preservation crossover (PPX) which is regarded as one of the better crossover operators and propose an improved version, termed as improved precedence preservation crossover (IPPX). Experimental results reveal that our proposed approach finds the near-optimal solutions by optimizing multiple criteria simultaneously with better results and also reduces the execution time significantly.