SummaryNear‐fault ground motions containing high energy and large amplitude velocity pulses may cause severe damage to structures. The most widely used intensity measure (IM) is the elastic spectral acceleration at the fundamental period of the structure (Sa(T1)); however, Sa(T1) is not a sufficient IM with respect to the effects of the pulse‐like ground motions on structural response. For near‐fault ground motions, including pulse‐like and non–pulse‐like time histories, we propose a vector‐valued IM consisting of a new IM called instantaneous power (IP(T1)) and the Sa(T1). The IP(T1) is defined as the maximum power of the bandpass‐filtered velocity time series over a time interval of 0.5T1. The IP(T1) is period‐dependent because the velocity time series is filtered over a period range (0.2T1‐3T1). This allows the IP(T1) to represent the power of the near‐fault ground motions relevant to the response of the structure. Using two‐dimensional models of the 2‐ and 9‐story steel‐frame buildings, we show that the proposed [Sa(T1), IP(T1)] vector IM gives more accurate estimates of the maximum inter‐story drift and collapse capacity responses from near‐fault ground motions than using the vector IM consisting of the Sa(T1), the presence of the velocity pulse, and the period of the velocity pulse. Moreover, for the structures considered, for a given Sa(T1), the IP(T1) is more strongly correlated with structural damage from near‐fault ground motions than the combination of the velocity pulse and pulse period.