In large-scale wireless sensor networks (WSNs), nodes close to sink nodes consume energy more quickly than other nodes due to packet forwarding. A mobile sink is a good solution to this issue, although it causes two new problems to nodes: (i) overhead of updating routing information; and (ii) increased operating time due to aperiodic query. To solve these problems, this paper proposes an energy-efficient data collection method, Sink-based Centralized transmission Scheduling (SC-Sched), by integrating asymmetric communication and wake-up radio. Specifically, each node is equipped with a low-power wake-up receiver. The sink node determines transmission scheduling, and transmits a wake-up message using a large transmission power, directly activating a pair of nodes simultaneously which will communicate with a normal transmission power. This paper further investigates how to deal with frame loss caused by fading and how to mitigate the impact of the wake-up latency of communication modules. Simulation evaluations confirm that using multiple channels effectively reduces data collection time and SC-Sched works well with a mobile sink. Compared with the conventional duty-cycling method, SC-Sched greatly reduces total energy consumption and improves the network lifetime by 7.47 times in a WSN with 4 data collection points and 300 sensor nodes.