This paper is aimed at developing a novel remotepaging system called Adaptive Grid Remote Pager (AGRP) on computational grids. Different to related work, this system is able to promise the effectiveness of remote paging. To achieve this goal, the resource broker of AGRP allocates only the grid nodes which are helpful for the performance of user programs to play the memory servers of remote paging. On the other hand, the memory servers automatically adapt their memory utilization through page migration to avoid the negative impact of memory competition from the local jobs at their execution nodes. Moreover, the memory clients always select the best one from their corresponding memory servers for each page-out request to minimize the latency of remote paging. We have implemented the proposed system in this paper. Our experimental results show that the proposed system indeed can dramatically improve the execution performance of the test program due to a significant reduction of the remote-paging latency and the avoidance in memory competition.