This work presents a Genetic Algorithm (GA) approach to Ground Station (GS) and Spacecraft (SC) Scheduling problem, which is based on the space missions and ground stations from ESA (European Space Agency). Genetic Algorithm has been used for optimization for many years. The first part of the work is to study how GA has been developed and put in position to science and engineering field. A general GA process is been introduced in this section, which describes basic operations of encoding, mutation, crossover, and selection. There are strengths and limitations of Genetic Algorithms for optimization, which are describe in this section too. The GS-SC scheduling problem is a highly resource-constrained. So in section 1.2, the concept of Resource-Constrained Schedule is studied and defined. And the difficulties of this kind of schedule are presented. The second part of the work defines the basic concepts of ground stations and spacecrafts, which is based on ESA examples. A mathematical model of Ground Stations and spacecrafts is built based on the definitions and assumption of the system. It is simplified so that it can be understood and modeled easily. There are three parts of the model: inputs, outputs and intermediate parameters. The system is to take the input data of spacecraft access windows and time requirements, and using an algorithm to generate a valid schedule solution. STK (Satellite Tool Kit) is been selected for data generation of this work. Space mission of selected ones are simulated and executed. The STK generates one of the important input data: Access Window information of GSs to all SCs. Together with defined mission requirement data, they are converted and stored in the schedule system using a pre-defined structure, which is waiting for further GA process. The GA process is the core chapter in this work. It describes the most important part of work that is approaching the solution of the entire problem. It starts from the encoding method, where two encoding methods are invested and tested, binary vector encoding and decimal vector encoding. It has been proved in this work that the decimal encoding has a better performance and computation speed than the other one. There are advantages and weaknesses that are both examined. Also crossover and mutation methods are introduced. The focus of this designated GA is on designing its fitness functions. This task is related with the constraints and objectives for the ground stations and space mission requirements. A technique of Fitness Modules (FM) is been developed to satisfying the varieties of mission objects. Those modules can be sequential or parallel in the fitness evaluation process. The introducing of FM concept gives the answer to add and remove mission objectives without affecting the existing GA fitness functions. Thus the final evaluating fitness is by summarizing all FMs with different weights. In this simplified model four FMs that represent four mission objectives are designed, these are, Fitness for Spacecraft Access Windows, Fitness for Communication Clashes, Fitness for Communication Time Requirement, and Fitness for Maximizing Ground Station Usage. Every GA needs a selection method of choosing chromosomes for population reproduction. There are some traditional selection methods, which are selected, described and studied. Also we have proposed a combinational selection method to accelerate the population fitting value. The last part of the work is to simulate the entire process in computer environment. Matlab is selected because of its excellent mathematical calculations capability. The GA is coded and executed with multiple times, in order to get the average results. Those data are all been illustrated. And one of the best schedules is been generated as the solution of the problem. The designed GA solved defined problem successfully. In the end, the weakness of this GA is mentioned, and future work direction is pointed out.