The data gathering problem is an important issue in wireless sensor networks (WSNs). In general, mobile elements are used to collect the sensed data of sensors to reduce the problem of unbalanced energy consumption caused by multi-hop transmission. However, in time-sensitive applications of WSNs where mobile elements are used to collect time-sensitive data, we must pay particular attention to the length of the traveling path to ensure that data are still useful after delivered to the sink. In this paper, we focus on how to plan a traveling path that meets the delay requirement of time-sensitive applications for data collection and reduces the amount of relay packets in the WSNs. The proposed algorithm is called Timeliness Traveling Path Planning (TTPP) algorithm. Based on the least squares curve approach, the proposed TTPP algorithm can find the best-fitting curve for any given set of sensors by reducing the amount of relay packets in the WSNs. The effectiveness of the proposed TTPP algorithm is confirmed through extensive simulations.