To overcome the limitations of Neural Programmer-Interpreters (NPI) in its universality and learnability, we propose the incorporation of combinator abstraction into neural programing and a new NPI architecture to support this abstraction, which we call Combinatory Neural Programmer-Interpreter (CNPI). Combinator abstraction dramatically reduces the number and complexity of programs that need to be interpreted by the core controller of CNPI, while still allowing the CNPI to represent and interpret arbitrary complex programs by the collaboration of the core with the other components. We propose a small set of four combinators to capture the most pervasive programming patterns. Due to the finiteness and simplicity of this combinator set and the offloading of some burden of interpretation from the core, we are able construct a CNPI that is universal with respect to the set of all combinatorizable programs, which is adequate for solving most algorithmic tasks. Moreover, besides supervised training on execution traces, CNPI can be trained by policy gradient reinforcement learning with appropriately designed curricula.