As an important strategy for reducing access time, balancing overload, and obtaining high data availability, replication is widely used in distributed systems such as data grids. Currently grid researchers often consider replica management problem from the viewpoint of whole systems, ignoring individual QoS requirements of each single request. With the rapid growth of QoS-sensitive data grid applications, fulfilling QoS requirements of every request becomes a big challenge. In this paper, a new problem called individual QoS-restricted replica placement problem is defined, which is proved to be NP-hard. As traditional methods cannot solve such problem, a QoS-restricted data grid model named IQDG is then built. Based on IQDG, a novel replica placement algorithm called qGREP is presented. The algorithm utilizes profit value as heuristic information, which considers both the fulfillment of individual QoS-restriction and the diversification of replica cost. In order to guarantee replica consistency, a logical ring-based updating mechanism is also proposed. IQDG takes individual QoS requirements of each request into account, and obtains rational replica policy by achieving tradeoff between the consistency cost and the access efficiency. Analysis reveals the internal relationship between network topology, user access pattern and overload. Experiments show that the model and algorithm are feasible and effective in complex data grid environment and can achieve good performance under different simulating conditions.