Exploiting sink mobility for balancing the energy dissipation of sensor nodes and preventing energy holes is a growing trend in the field of wireless sensor network (WSN). The mobile sink moves throughout the network and collects data in a single-hop fashion resulting in less energy consumption of the sensor nodes. Despite the advantage of this scheme, data forwarding to the mobile sink during an emergency situation is a major issue that should be dealt with. For efficient data delivery within the stipulated deadline, the sensor node which has sensed a delay-intolerant data needs to forward the data towards the mobile sink. In this paper, a Moore curve based trajectory of the mobile sink has been considered for efficient sink based data collection. This work is also motivated by anycast forwarding of delay sensitive data to the mobile sink before the sensed data lose its relevance, where the node follows a strict sleep-wake pattern. We have evaluated the effectiveness of the proposed trajectory based data collection scheme by simulation using MATLAB. The delay-intolerant data routing scheme (DRS) shows that the data reaches the mobile sink within the given deadline while restricting the energy dissipation of the sensor nodes to a minimum. This have been verified by extensive simulations which show that when compared to static sink, the usage of a mobile sink improves the network lifetime by almost 12%. This work has also been compared with an existing work (PMDD) to show its validity. The simulation results depict that DRS shows an improvement of about 25%–29% in terms of network lifetime.