The design of Data Grids allows grid facilities to manage data files and their corresponding replicas from all around the globe. Replica selection in Data Grids is a complex service that selects the best replica place amongst several scattered places based on quality of service parameters. All replica selection algorithms look for the best replica for the requesting users without taking into account the limitation of their network or hardware capabilities to find the best fit. This leaves capable users with limited ability to connect with the best replica places without fully utilizing their download speed. It furthermore compromises the best replica places and shifts capable users to lower quality replica places and degrades the whole Data Grid environment. To improve quality of service parameters the solution we propose is, a matching algorithm that matches the capabilities of grid user with replica providers that are the best fit. This best-fit approach takes into account both the capabilities of grid users and the capabilities of replica places and creates matches of almost similar capabilities. Simulation results proved that the best-fit algorithm outperforms previous replica selection algorithms.