Mobile grid is a combination of grid computing and mobile computing to build grid systems in a wireless mobile environment. The development of network technology is assisting in realizing mobile grid. Mobile grid based on established grid infrastructures needs effective resource management and reliable job scheduling because mobile grid utilizes not only static grid resources but also dynamic grid resources with mobility. However, mobile devices are considered as unavailable resources in traditional grids. Mobile resources should be integrated into existing grid sites. Therefore, this paper presents a mobile grid middleware interconnecting existing grid infrastructures with mobile resources and a mobile service agent installed on the mobile resources. This paper also proposes a mobile resource reliability-based job scheduling model in order to overcome the unreliability of wireless mobile devices and guarantee stable and reliable job processing. In the proposed job scheduling model, the mobile service agent calculates the mobile resource reliability of each resource by using diverse reliability metrics and predicts it. The mobile grid middleware allocated jobs to mobile resources by predicted mobile resource reliability. We implemented a simulation model that simplifies various functions of the proposed job scheduling model by using the DEVS (Discrete Event System Specification) which is the formalism for modeling and analyzing a general system. We also conducted diverse experiments for performance evaluation. Experimental results demonstrate that the proposed model can assist in improving the performance of mobile grid in comparison with existing job scheduling models.