An innovative generative design strategy, based on shape grammar, is proposed for the minimum-weight design of diagrid tall buildings. By considering the building as a three-dimensional vertical cantilever beam with a tubular section under horizontal load, it is evident that bending and shear stiffness demands vary along the width and elevation of the building. Further, while the structural design of tall buildings is usually governed by stiffness, the predominant design criterion for diagrids could be the local strength demand, especially for low slenderness values, thanks to the inherent rigidity of the triangular pattern. Starting from these considerations, in this paper, a generative design strategy is proposed, able to find diagrid patterns that accommodate the differentiated stiffness demand along width/elevation and satisfy the predominant design criterion, stiffness or strength. The design strategy is applied to tall building models characterised by different slenderness values. The comparison to diagrid patterns analysed in previous literature works in terms of structural weight and performance parameters highlights the effectiveness of the design strategy and the efficiency of the generated patterns.