As a novel Internet architecture, Named Data Networking (NDN) shifts the communication model from address-centric to content-centric. An NDN router caches the data in its content store, greatly reducing network traffic. NDN adopts the hierarchical naming schema, which allows the name aggregation and enables high scalability. However, in a richly connected topology, the nearest data replica are often not on the path dictated by NDN's tree-like data fetching model. This might result in a lower data delivery efficiency compared with the flat self-certifying naming schema in other Information-Centric Networking (ICN) architectures. To address the low efficiency problem, we propose a CDN-like enhancement to the NDN design, called Fetching the Nearest Replica (FNR). In FNR, when a consumer sends an interest for a popular data, the data is fetched from the nearest replica in the network, regardless of whether it is on the best path from the producer to the consumer. We present the design details and theoretical overhead analysis for FNR. Our evaluation results using ndnSIM simulator show that on average FNR reduces the total (inter-domain, intra-domain) traffic by 25.6% (53.0%, 18.2%) on average, compared to the default NDN approach. In addition, the average latency is reduced by 37% and the average cost is reduced by 51.4%. To the best of our knowledge, this paper is the first NDN enhancement in the literature to support nearest replica fetching in NDN.