We present an approximation framework for attacking the undecidable termination problem of logic programs, as an alternative to current termination/non-termination proof approaches. We introduce an idea of termination prediction, which predicts termination of a logic program in case that neither a termination nor a non-termination proof is applicable. We establish a necessary and sufficient characterization of infinite (generalized) SLDNF-derivations with arbitrary (concrete or moded) queries, and develop an algorithm that predicts termination of general logic programs with arbitrary queries. We have implemented a termination prediction system and obtained quite satisfactory experimental results. Our prediction is 100% correct for all benchmark programs of the Termination Competition 2007, of which eighteen programs cannot be proved by the existing state-of-the-art analyzers like AProVE07, NTI, Polytool and TALP.