For most software systems it is very hard to obtain expected output automatically on the basis of specifications. However, there exist many notable detection points in output domain of some software, so it may be more suitable to develop test cases from output domain than from input. In addition, even if an output is given, it is also difficult to find its input automatically. Therefore in this paper, we present an output domain based automatic test case generation method. At first, a back propagation neural network is used to create a model that can be taken as a function substitute for the software under test, and then according to the created function model, genetic algorithms are employed to search the corresponding inputs for given outputs. In order to improve the effectiveness of test case generation, a new crossover operation and a mutation operation are introduced in our genetic algorithm. Moreover, a number of experiments have been conducted on test generation based on the created function models over the fault tolerant software RSDIMU and three common used software. The experimental results show that the approach is promising and effective, and our genetic algorithm can distinctly enhance the efficiency and successful ratio to test case generation from output domains.