Thermally conductive polymer composites are of great interest for a variety of applications. One strategy to enhance the composite thermal conductivity is to minimize the thermal resistance at numerous contacts and interfaces inside the composites. Recently, it has been shown that the thermal boundary resistance between silver nanowires (AgNWs) and polyvinylpyrrolidone (PVP) is significantly lower than that between nonmetallic nanofillers such as carbon nanotubes and various polymers. To demonstrate that AgNWs could serve as effective fillers for thermally conductive composites, here we report on preparation and characterization of AgNW-PVP composite thin films. A layered assembly technique, which allows for the embedded filler network to largely align along the in-plane direction, has been adopted to prepare composite films of various AgNW volume fractions. Thermal measurements show that the combined effects of aligned AgNWs and low AgNW-PVP interfacial thermal resistance lead to remarkably enhanced in-plane thermal conductivity. At an AgNW volume fraction of 0.2, the composite thermal conductivity reaches 27.2 W/(m·K), which represents more than 2 orders of magnitude enhancement as compared to that of the corresponding neat polymer. Importantly, analyses disclose a nonmonotonic trend for the effective thermal conductivity of the AgNW network, which could be due to the more significant contact resistance at a higher AgNW loading level. This study provides insights into manufacturing highly thermally conductive polymer composites for thermal management applications.