Robotic multi-pass welding for thick and shape-varying weld geometry is a challenging problem. To achieve good weld quality, desired welding profile for the whole welding bevel is necessary, which requires the welding inputs to be changed appropriately in real-time. In this paper, a welding profile control with data-driven fast input allocation (PC-FIA) algorithm is proposed for robotic multi-pass welding on a shape-varying weld geometry, namely, TYK pipe-to-pipe joint. Firstly, the H∞ control algorithm is used for the welding profile control in order to suppress the error propagation during the multi-pass welding. Secondly, the welding input parameters including torch traveling speed and weaving parameters are allocated using a max−min optimization based on the identified weld input constraint from a data-driven approach. Experimental results show that the weld profile using the proposed method achieves 60% decrease of root-mean-square error with respect to the planned reference, as compared to the case of without using the proposed PC-FIA method. In addition, the allocated weaving parameters ensure that the welding inputs are always maintained within the polyhedral constraint and the whole welding quality is acceptable by industry standard.