A Content Delivery Network (CDN) is a distributed network of servers (that provide web content) and file storage devices deployed in various geographical locations such that when requests are being made by users, these requests are redirected via GEO-DNS to the closest content repository to the user for response. This work proposes an adaptive request routing algorithm to choose the replica server using network proximity and a combination of Quality of Service metrics. The metrics include: bandwidth, availability of server, and latency. This is because the original intention of CDNs is for surrogate servers to respond to request from clients that are closer in proximity. This is not always the best option because the closest surrogate may either be overloaded (making it unavailable) or the connection may be poor. Thus, proximity with a mixture of metric are combined to choose the best surrogate to respond to request. . In contrast to most works in existing literature, this study employs three metrics and five membership functions (Very high, High, Medium, Low and Very low) based on the rules guiding fuzzy logic to give an accurate measure for each of the three metrics used in order to determine without errors when to grant or deny a request from the users. This makes it an improvement on existing works that used some other metrics and only three membership functions (High, Medium and Low), this research uses two additional membership functions which help to give a more precise measure of the variables in question and hence improves the efficiency of the request delivery, thus giving users of the network more robust information as regards the quality of web content service delivery.