Intelligent Grid computing is considered as an essential infrastructure in future life, and they are executed and implemented to save the energy, to reduce the costs and to increase reliability. This study has been carried out with the aim of identifying various samples of Grid networks and investigating the applied and functional fields. In this way, science and technology develops and expands through identifying their weaknesses and attempting to remove these weaknesses and to solve the problems. In addition, the purpose is to increase the reliability in grid networks for using the services. In fact, the purpose of this study is to provide and present a compact and intensive mathematical tool by using Petri nets in order to analyze reliability and certainty in Grid networks. In this study, reliability is investigated in Grid services, and through using Petri nets, a model is represented and proposed for computing as well as increasing reliability in Grid networks. In this research, a new model has been introduced for increasing reliability in Grid networks. In this model, by using series-parallel mode and also by adding redundancy technique to the system, reliability has been considerably improved.