This study concerns sloshing problems of free-surface liquids in moving containers [1] and parameterized reduced-order modeling (ROM) [2] using Isogeometric Analysis (IGA) [3]. These analyses are crucial in aerospace applications to estimate the free-surface elevation and reaction loads acting on liquid-filled tanks. The resulting ROM can then be used in fluid-structure simulations, accounting for the elasticity of the container. The challenge consists in constructing a ROM that incorporates a geometrical parameterization of the liquid domain inside a rigid tank as a function of liquid height. In ROM approaches, geometrical parameters prevent the precomputation of reduced operators, making hyper-reduction techniques necessary (e.g., energy conservation sample weights [4]). IGA enables the parameterization of a mapping of geometry as a function of liquid height. The originality of this work lies in the development of a parameterized ROM for fast and accurate linear sloshing analyses in both the frequency and time domains using IGA. The methodology is as follows. First, a 3D geometrical parameterization of the liquid domain is established based on the positions of control points and associated weights. Thus, the mapping between a reference configuration and various current geometrical domains is directly obtained using NURBS discretization. Parameterized operators are then mapped onto a unique fluid domain for integration. The ROM approach consists of two steps: (i) generating a basis either from various sloshing modal analyses or snapshots from high-dimensional model (HDM) time-domain integration and (ii) constructing the ROM using a projection-based approach and hyper-reduction techniques. A comparison of quantities of interest between HDM and ROM will be conducted, considering both the speed-up factor and accuracy.