Due to the superiority in similarity computation and database storage for large-scale multiple modalities data, cross-modal hashing methods have attracted extensive attention in similarity retrieval across the heterogeneous modalities. However, there are still some limitations to be further taken into account: (1) most current CMH methods transform real-valued data points into discrete compact binary codes under the binary constraints, limiting the capability of representation for original data on account of abundant loss of information and producing suboptimal hash codes; (2) the discrete binary constraint learning model is hard to solve, where the retrieval performance may greatly reduce by relaxing the binary constraints for large quantization error; (3) handling the learning problem of CMH in a symmetric framework, leading to difficult and complex optimization objective. To address above challenges, in this paper, a novel Asymmetric Correlation Quantization Hashing (ACQH) method is proposed. Specifically, ACQH learns the projection matrixs of heterogeneous modalities data points for transforming query into a low-dimensional real-valued vector in latent semantic space and constructs the stacked compositional quantization embedding in a coarse-to-fine manner for indicating database points by a series of learnt real-valued codeword in the codebook with the help of pointwise label information regression simultaneously. Besides, the unified hash codes across modalities can be directly obtained by the discrete iterative optimization framework devised in the paper. Comprehensive experiments on diverse three benchmark datasets have shown the effectiveness and rationality of ACQH.