Cross-laminated timber (CLT) is an innovative engineered timber product and has been widely used for constructing tall timber buildings due to its excellent structural performance and good strength with its multi-layers of boards in both perpendicular directions. However, the global serviceability performance of tall timber buildings constructed from CLT products for the lift core, walls, and floors under wind load is not well known yet, even though it is crucial in a design. In this study, the finite element software SAP2000 is used to numerically simulate the global static and dynamic serviceability behaviours of a 30-storey tall CLT building assumed in Glasgow, Scotland, UK. The maximum horizontal storey displacement due to wind is only 16.6% of the design limit and the maximum global horizontal displacement is only 13.8% of the limit set to the Eurocodes. The first three lowest vibrational frequencies, modes and shapes were obtained, with the fundamental frequency being 19.9% larger than the code-recommended value. Accordingly, the peak acceleration of the building due to wind was determined as per the Eurocodes and ISO standard. The results show that the global serviceability behaviours of the building satisfy the requirements of the Eurocodes and other design standards. Parametric studies on the peak accelerations of the tall CLT building were also conducted by varying the timber material properties and building masses. By increasing the timber grade for CLT members, the generalised building mass and the generalised building stiffness can all be adopted to lower the peak accelerations at the top level of the building, so as to reduce human perceptions of the wind-induced vibrations with respect to the peak acceleration.