In the neighborhood rough sets, the attribute reduction based on information measures holds fundamental research value and application significance. However, the conditional neighborhood entropy exhibits granulation non-monotonicity, so its attribute reduction has the research difficulty and application limitation. Aiming at this issue, by virtue of the granular computing technology and its relevant three-layer granular structure, a novel conditional neighborhood entropy with granulation monotonicity is constructed, and its relevant attribute reduction is further investigated. At first, the granulation non-monotonicity and its roots of the conditional neighborhood entropy are revealed; then, the three-layer granular structure is adopted to construct a new conditional neighborhood entropy by the bottom-up strategy, and the corresponding granulation monotonicity is gained; furthermore, relevant attribute reduction and its heuristic reduction algorithm are studied, according to this proposed information measure with the granulation monotonicity; finally, data experiments based on the UCI (University of CaliforniaIrvine) machine learning repository are implemented, and thus they verify both the granulation monotonicity of the constructed conditional neighborhood entropy and the calculation effectiveness of the related heuristic reduction algorithm. As shown by the obtained results, the established conditional neighborhood entropy has the granulation monotonicity to improve the conditional neighborhood entropy, and its induced attribute reduction has broad application prospects.