Glued-laminated timber (Glulam) is an innovative engineered timber product and has been widely used for constructing spatial grand timber structures and tall timber buildings due to its exceptional natural attraction, easy processing, decent fire resistance and outstanding structural performance. However, global serviceability performances of tall timber buildings constructed from Glulam products for beams, columns and bracings and CLT products for lift core and floors under wind load are not well known yet though they are crucial in structural design and global analysis. In this study, finite element software SAP2000 is used to numerically simulate the global static and dynamic serviceability behaviours of a 105 m high 30-storey tall Glulam building with CLT lift core and floors assumed in Glasgow, Scotland, UK. The maximum horizontal storey displacement due to wind is 58.5% of the design limit and the maximum global horizontal displacement is 49.7% of the limit set to the Eurocodes. The first three lowest vibrational frequencies, modes and shapes of the building are obtained, with the fundamental frequency being 33.3% smaller than the code recommended value due to its low mass and stiffness. The peak acceleration of the building due to wind is determined to the Eurocodes and ISO 10137. 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 Glulam building are also conducted by varying timber material properties and building masses. 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 the human perceptions to the wind induced vibrations with respect to the peak acceleration.