For laminated composite structures as key components of storage tanks serving at cryogenic temperature, it is crucial to identify the damage mechanisms for evaluating their mechanical properties and guiding structural design. In this work, the cryogenic tensile damage behavior of a thin-walled woven composite laminate was investigated through the acoustic emission (AE) monitoring and multiscale finite element (FE) computation at typical low temperatures of 153 K, 77 K and 20 K. We first established temperature-dependent constitutive laws for the microscale and mesoscale constituents of such composites based on experimental data, followed by the development of a hierarchical computational framework for modeling multiscale damage characteristics at different low temperatures. A fiber-optic acoustic emission measurement system was constructed to provide online monitoring of tensile damage of the woven composite laminates at cryogenic temperatures as low as 20 K. The comparations were made between the predicted cryogenic damage characteristics and in-situ AE signal analysis, assisted by scanning electron microscope (SEM) observations. The computed cryogenic damage evolution closely matched the AE signal identification results. The results indicate that fiber breakage and matrix cracking are the dominant cryogenic damage modes, and that the different low temperatures exert significant effects on the properties of the epoxy matrix, yarns and composite laminates. The combination of the AE monitoring system and the computational scheme provides a valuable tool for evaluating structural integrity and guiding the microstructural design of composite laminates used in cryogenic environments.