Mastering thermal-hydraulic characteristics of the once-through steam generator (OTSG) is essential for ensuring the stable operation and safety of reactors. While refined simulation models offer relatively accurate predictions for OTSG thermal-hydraulic research, the high computational cost often limits their applicability in system online- monitoring and real-time control. Specifically, the computational burden of these models can be prohibitive for multi-query simulation tasks such as optimization design and uncertainty analysis. Model order reduction (MOR) provides a solution that meets the need for both precision and speed in nuclear reactor system. Proper orthogonal decomposition (POD), as one of the representative MOR methods, has been widely used in reactor-related research, but the data-driven reduced order model (ROM) shows poor robustness when applied to situations that deviate from the modeling conditions. Therefore, a parametric ROM suitable for estimating the thermal and hydraulic characteristics of OTSG is established in this work by introducing double POD (DPOD). The model is verified based on the full-order model (FOM) developed in the RELAP5 code. Verification results demonstrate that the maximum relative error between the ROM estimations and FOM data is less than 0.5%, while the computational time of the ROM is less than 0.1 s. This parametric ROM thus satisfies the requirements for efficient and accurate estimation of OTSG thermal-hydraulic characteristics, providing a viable alternative to refined simulation models for multi-query simulation tasks and supporting for nuclear digital twins.