Proactive content caching at user devices and coded delivery is studied for a non-uniform file popularity distribution. A novel centralized uncoded caching and coded delivery scheme, called cross-level coded delivery (CLCD) , is proposed, which can be applied to large file libraries under non-uniform demands. In the CLCD scheme, the same sub-packetization is used for all the files in the library in order to prevent additional zero-padding in the delivery phase, and unlike the existing schemes in the literature, users requesting files from different popularity groups can still be served by the same multicast message in order to reduce the delivery rate. Simulation results indicate more than 10% reduction in the average delivery rate for typical Zipf distribution parameter values.