Abstract: High-rise concrete structures are long and flexible cantilever structures which are commonly used as chimneys, water towers and TV towers. The existing earthquake intensity measures (IMs) mainly focus on building structures under one-dimensional or two-dimensional input ground motions, but high-rise concrete structures are sensitive to vertical ground motions. Based on a chimney and a water tower, it proposes a combined earthquake intensity measure which considers both the higher-mode effect and period elongation effect. The sufficiency and efficiency of the IM are investigated for three-dimensional far-field ground motions and near-fault ground motions with the pulse-like effect. A comparison is made among fifteen existing IMs, and the results indicate that the proposed IM is suitable for such kind of structures. Consequently, this IM is a promising intensity measure in the seismic assessment of high-rise structures under three-dimensional ground motions.