We propose a time-efficient local data aggregation algorithm that aggregates delay-constrained data within a given time deadline in clustered wireless sensor networks. Our approach consists of two phases. First, we design a zone-based fast data aggregation tree (ZFDAT) to eliminate unnecessary packets being forwarded to many receiver nodes and avoid long detour paths until cluster-head, where cluster-head is local control center to coordinate the data transmissions in the cluster. Next, we propose optimal link scheduling algorithm to minimize aggregation time by given variable length of time slots for all links in the ZFDAT. Our simulation results show that our approach can minimize the aggregation time under energy constraint and outperforms the similar existing algorithms. In particular, our approach distributes the total aggregation time, then it can also reduce the heavy processing load at the cluster-head.