In large e-commerce platforms, search systems are typically composed of a series of modules, including recall, pre-ranking, and ranking phases. The pre-ranking phase, serving as a lightweight module, is crucial for filtering out the bulk of products in advance for the downstream ranking module. Industrial efforts on optimizing the pre-ranking model have predominantly focused on enhancing ranking consistency, model structure, and generalization towards long-tail items. Beyond these optimizations, meeting the system performance requirements presents a significant challenge. Contrasting with existing industry works, we propose a novel method: a Generalizable and RAnk-ConsistEnt Pre-Ranking Model (GRACE), which achieves: 1) Ranking consistency by introducing multiple binary classification tasks that predict whether a product is within the top-k results as estimated by the ranking model, which facilitates the addition of learning objectives on common point-wise ranking models; 2) Generalizability through contrastive learning of representation for all products by pre-training on a subset of ranking product embeddings; 3) Ease of implementation in feature construction and online deployment. Our extensive experiments demonstrate significant improvements in both offline metrics and online A/B test: a 0.75% increase in AUC and a 1.28% increase in CVR.